Solución
sin2(x)+sin22(x)+sin23(x)=1
Solución
x=23π+2πn,x=1.12079…+2πn,x=π−1.12079…+2πn
+1
Grados
x=270∘+360∘n,x=64.21666…∘+360∘n,x=115.78333…∘+360∘nPasos de solución
sin2(x)+sin22(x)+sin23(x)=1
Usando el método de sustitución
sin2(x)+sin22(x)+sin23(x)=1
Sea: sin(x)=uu2+u22+u23=1
u2+u22+u23=1:u=−1,u≈0.90044…,u≈−1.03277…
u2+u22+u23=1
Mover 1al lado izquierdo
u2+u22+u23=1
Restar 1 de ambos ladosu2+u22+u23−1=1−1
Simplificaru2+u22+u23−1=0
u2+u22+u23−1=0
Escribir en la forma binómica anxn+…+a1x+a0=0u23+u22+u2−1=0
Factorizar u23+u22+u2−1:(u+1)(u22+u−1)
u23+u22+u2−1
Utilizar el teorema de la raíz racional
a0=1,an=1
Los divisores de a0:1,Los divisores de an:1
Por lo tanto, verificar los siguientes numeros racionales:±11
−11 es la raíz de la expresión, por lo tanto, factorizar u+1
=(u+1)u+1u23+u22+u2−1u+1u23+u22+u2−1=u22+u−1
u+1u23+u22+u2−1
Dividir u+1u23+u22+u2−1:u+1u23+u22+u2−1=u22+u+1u2−1
Dividir los coeficientes de los términos de mayor grado del numerador u23+u22+u2−1
y el divisor u+1:uu23=u22
Cociente=u22Multiplicar u+1 por u22:u23+u22Substraer u23+u22 de u23+u22+u2−1 para obtener un nuevo residuoResiduo=u2−1
Por lo tantou+1u23+u22+u2−1=u22+u+1u2−1
=u22+u+1u2−1
Dividir u+1u2−1:u+1u2−1=u+u+1−u−1
Dividir los coeficientes de los términos de mayor grado del numerador u2−1
y el divisor u+1:uu2=u
Cociente=uMultiplicar u+1 por u:u2+uSubstraer u2+u de u2−1 para obtener un nuevo residuoResiduo=−u−1
Por lo tantou+1u2−1=u+u+1−u−1
=u22+u+u+1−u−1
Dividir u+1−u−1:u+1−u−1=−1
Dividir los coeficientes de los términos de mayor grado del numerador −u−1
y el divisor u+1:u−u=−1
Cociente=−1Multiplicar u+1 por −1:−u−1Substraer −u−1 de −u−1 para obtener un nuevo residuoResiduo=0
Por lo tantou+1−u−1=−1
=u22+u−1
=(u+1)(u22+u−1)
(u+1)(u22+u−1)=0
Utilizando el teorema de factor cero: si ab=0entonces a=0o b=0u+1=0oru22+u−1=0
Resolver u+1=0:u=−1
u+1=0
Mover 1al lado derecho
u+1=0
Restar 1 de ambos ladosu+1−1=0−1
Simplificaru=−1
u=−1
Resolver u22+u−1=0:u≈0.90044…,u≈−1.03277…
u22+u−1=0
Encontrar una solución para u22+u−1=0 utilizando el método de Newton-Raphson:u≈0.90044…
u22+u−1=0
Definición del método de Newton-Raphson
f(u)=u22+u−1
Hallar f′(u):22u21+1
dud(u22+u−1)
Aplicar la regla de la suma/diferencia: (f±g)′=f′±g′=dud(u22)+dudu−dud(1)
dud(u22)=22u21
dud(u22)
Aplicar la regla de la potencia: dxd(xa)=a⋅xa−1=22u22−1
Simplificar=22u21
dudu=1
dudu
Aplicar la regla de derivación: dudu=1=1
dud(1)=0
dud(1)
Derivada de una constante: dxd(a)=0=0
=22u21+1−0
Simplificar=22u21+1
Sea u0=1Calcular un+1 hasta que Δun+1<0.000001
u1=0.95652…:Δu1=0.04347…
f(u0)=122+1−1=1f′(u0)=22⋅121+1=23u1=0.95652…
Δu1=∣0.95652…−1∣=0.04347…Δu1=0.04347…
u2=0.92205…:Δu2=0.03446…
f(u1)=0.95652…22+0.95652…−1=0.33260…f′(u1)=22⋅0.95652…21+1=9.64996…u2=0.92205…
Δu2=∣0.92205…−0.95652…∣=0.03446…Δu2=0.03446…
u3=0.90410…:Δu3=0.01795…
f(u2)=0.92205…22+0.92205…−1=0.08979…f′(u2)=22⋅0.92205…21+1=5.00231…u3=0.90410…
Δu3=∣0.90410…−0.92205…∣=0.01795…Δu3=0.01795…
u4=0.90055…:Δu4=0.00354…
f(u3)=0.90410…22+0.90410…−1=0.01294…f′(u3)=22⋅0.90410…21+1=3.64850…u4=0.90055…
Δu4=∣0.90055…−0.90410…∣=0.00354…Δu4=0.00354…
u5=0.90044…:Δu5=0.00010…
f(u4)=0.90055…22+0.90055…−1=0.00037…f′(u4)=22⋅0.90055…21+1=3.43859…u5=0.90044…
Δu5=∣0.90044…−0.90055…∣=0.00010…Δu5=0.00010…
u6=0.90044…:Δu6=9.96449E−8
f(u5)=0.90044…22+0.90044…−1=3.42017E−7f′(u5)=22⋅0.90044…21+1=3.43236…u6=0.90044…
Δu6=∣0.90044…−0.90044…∣=9.96449E−8Δu6=9.96449E−8
u≈0.90044…
Aplicar la división larga Equation0:u−0.90044…u22+u−1=u21+0.90044…u20+0.81080…u19+0.73008…u18+0.65739…u17+0.59195…u16+0.53302…u15+0.47995…u14+0.43217…u13+0.38914…u12+0.35040…u11+0.31552…u10+0.28411…u9+0.25582…u8+0.23035…u7+0.20742…u6+0.18677…u5+0.16818…u4+0.15143…u3+0.13636…u2+0.12278…u+1.11056…
u21+0.90044…u20+0.81080…u19+0.73008…u18+0.65739…u17+0.59195…u16+0.53302…u15+0.47995…u14+0.43217…u13+0.38914…u12+0.35040…u11+0.31552…u10+0.28411…u9+0.25582…u8+0.23035…u7+0.20742…u6+0.18677…u5+0.16818…u4+0.15143…u3+0.13636…u2+0.12278…u+1.11056…≈0
Encontrar una solución para u21+0.90044…u20+0.81080…u19+0.73008…u18+0.65739…u17+0.59195…u16+0.53302…u15+0.47995…u14+0.43217…u13+0.38914…u12+0.35040…u11+0.31552…u10+0.28411…u9+0.25582…u8+0.23035…u7+0.20742…u6+0.18677…u5+0.16818…u4+0.15143…u3+0.13636…u2+0.12278…u+1.11056…=0 utilizando el método de Newton-Raphson:u≈−1.03277…
u21+0.90044…u20+0.81080…u19+0.73008…u18+0.65739…u17+0.59195…u16+0.53302…u15+0.47995…u14+0.43217…u13+0.38914…u12+0.35040…u11+0.31552…u10+0.28411…u9+0.25582…u8+0.23035…u7+0.20742…u6+0.18677…u5+0.16818…u4+0.15143…u3+0.13636…u2+0.12278…u+1.11056…=0
Definición del método de Newton-Raphson
f(u)=u21+0.90044…u20+0.81080…u19+0.73008…u18+0.65739…u17+0.59195…u16+0.53302…u15+0.47995…u14+0.43217…u13+0.38914…u12+0.35040…u11+0.31552…u10+0.28411…u9+0.25582…u8+0.23035…u7+0.20742…u6+0.18677…u5+0.16818…u4+0.15143…u3+0.13636…u2+0.12278…u+1.11056…
Hallar f′(u):21u20+18.00890…u19+15.40523…u18+13.14148…u17+11.17579…u16+9.47123…u15+7.99531…u14+6.71938…u13+5.61826…u12+4.66979…u11+3.85448…u10+3.15522…u9+2.55699…u8+2.04661…u7+1.61250…u6+1.24454…u5+0.93387…u4+0.67272…u3+0.45431…u2+0.27272…u+0.12278…
Sea u0=−5Calcular un+1 hasta que Δun+1<0.000001
u1=−4.76362…:Δu1=0.23637…
f(u0)=(−5)21+0.90044…(−5)20+0.81080…(−5)19+0.73008…(−5)18+0.65739…(−5)17+0.59195…(−5)16+0.53302…(−5)15+0.47995…(−5)14+0.43217…(−5)13+0.38914…(−5)12+0.35040…(−5)11+0.31552…(−5)10+0.28411…(−5)9+0.25582…(−5)8+0.23035…(−5)7+0.20742…(−5)6+0.18677…(−5)5+0.16818…(−5)4+0.15143…(−5)3+0.13636…(−5)2+0.12278…(−5)+1.11056…=−4.04069E14f′(u0)=21(−5)20+18.00890…(−5)19+15.40523…(−5)18+13.14148…(−5)17+11.17579…(−5)16+9.47123…(−5)15+7.99531…(−5)14+6.71938…(−5)13+5.61826…(−5)12+4.66979…(−5)11+3.85448…(−5)10+3.15522…(−5)9+2.55699…(−5)8+2.04661…(−5)7+1.61250…(−5)6+1.24454…(−5)5+0.93387…(−5)4+0.67272…(−5)3+0.45431…(−5)2+0.27272…(−5)+0.12278…=1.70942E15u1=−4.76362…
Δu1=∣−4.76362…−(−5)∣=0.23637…Δu1=0.23637…
u2=−4.53848…:Δu2=0.22513…
f(u1)=(−4.76362…)21+0.90044…(−4.76362…)20+0.81080…(−4.76362…)19+0.73008…(−4.76362…)18+0.65739…(−4.76362…)17+0.59195…(−4.76362…)16+0.53302…(−4.76362…)15+0.47995…(−4.76362…)14+0.43217…(−4.76362…)13+0.38914…(−4.76362…)12+0.35040…(−4.76362…)11+0.31552…(−4.76362…)10+0.28411…(−4.76362…)9+0.25582…(−4.76362…)8+0.23035…(−4.76362…)7+0.20742…(−4.76362…)6+0.18677…(−4.76362…)5+0.16818…(−4.76362…)4+0.15143…(−4.76362…)3+0.13636…(−4.76362…)2+0.12278…(−4.76362…)+1.11056…=−1.45042E14f′(u1)=21(−4.76362…)20+18.00890…(−4.76362…)19+15.40523…(−4.76362…)18+13.14148…(−4.76362…)17+11.17579…(−4.76362…)16+9.47123…(−4.76362…)15+7.99531…(−4.76362…)14+6.71938…(−4.76362…)13+5.61826…(−4.76362…)12+4.66979…(−4.76362…)11+3.85448…(−4.76362…)10+3.15522…(−4.76362…)9+2.55699…(−4.76362…)8+2.04661…(−4.76362…)7+1.61250…(−4.76362…)6+1.24454…(−4.76362…)5+0.93387…(−4.76362…)4+0.67272…(−4.76362…)3+0.45431…(−4.76362…)2+0.27272…(−4.76362…)+0.12278…=6.44244E14u2=−4.53848…
Δu2=∣−4.53848…−(−4.76362…)∣=0.22513…Δu2=0.22513…
u3=−4.32405…:Δu3=0.21442…
f(u2)=(−4.53848…)21+0.90044…(−4.53848…)20+0.81080…(−4.53848…)19+0.73008…(−4.53848…)18+0.65739…(−4.53848…)17+0.59195…(−4.53848…)16+0.53302…(−4.53848…)15+0.47995…(−4.53848…)14+0.43217…(−4.53848…)13+0.38914…(−4.53848…)12+0.35040…(−4.53848…)11+0.31552…(−4.53848…)10+0.28411…(−4.53848…)9+0.25582…(−4.53848…)8+0.23035…(−4.53848…)7+0.20742…(−4.53848…)6+0.18677…(−4.53848…)5+0.16818…(−4.53848…)4+0.15143…(−4.53848…)3+0.13636…(−4.53848…)2+0.12278…(−4.53848…)+1.11056…=−5.20633E13f′(u2)=21(−4.53848…)20+18.00890…(−4.53848…)19+15.40523…(−4.53848…)18+13.14148…(−4.53848…)17+11.17579…(−4.53848…)16+9.47123…(−4.53848…)15+7.99531…(−4.53848…)14+6.71938…(−4.53848…)13+5.61826…(−4.53848…)12+4.66979…(−4.53848…)11+3.85448…(−4.53848…)10+3.15522…(−4.53848…)9+2.55699…(−4.53848…)8+2.04661…(−4.53848…)7+1.61250…(−4.53848…)6+1.24454…(−4.53848…)5+0.93387…(−4.53848…)4+0.67272…(−4.53848…)3+0.45431…(−4.53848…)2+0.27272…(−4.53848…)+0.12278…=2.42801E14u3=−4.32405…
Δu3=∣−4.32405…−(−4.53848…)∣=0.21442…Δu3=0.21442…
u4=−4.11982…:Δu4=0.20423…
f(u3)=(−4.32405…)21+0.90044…(−4.32405…)20+0.81080…(−4.32405…)19+0.73008…(−4.32405…)18+0.65739…(−4.32405…)17+0.59195…(−4.32405…)16+0.53302…(−4.32405…)15+0.47995…(−4.32405…)14+0.43217…(−4.32405…)13+0.38914…(−4.32405…)12+0.35040…(−4.32405…)11+0.31552…(−4.32405…)10+0.28411…(−4.32405…)9+0.25582…(−4.32405…)8+0.23035…(−4.32405…)7+0.20742…(−4.32405…)6+0.18677…(−4.32405…)5+0.16818…(−4.32405…)4+0.15143…(−4.32405…)3+0.13636…(−4.32405…)2+0.12278…(−4.32405…)+1.11056…=−1.86884E13f′(u3)=21(−4.32405…)20+18.00890…(−4.32405…)19+15.40523…(−4.32405…)18+13.14148…(−4.32405…)17+11.17579…(−4.32405…)16+9.47123…(−4.32405…)15+7.99531…(−4.32405…)14+6.71938…(−4.32405…)13+5.61826…(−4.32405…)12+4.66979…(−4.32405…)11+3.85448…(−4.32405…)10+3.15522…(−4.32405…)9+2.55699…(−4.32405…)8+2.04661…(−4.32405…)7+1.61250…(−4.32405…)6+1.24454…(−4.32405…)5+0.93387…(−4.32405…)4+0.67272…(−4.32405…)3+0.45431…(−4.32405…)2+0.27272…(−4.32405…)+0.12278…=9.15059E13u4=−4.11982…
Δu4=∣−4.11982…−(−4.32405…)∣=0.20423…Δu4=0.20423…
u5=−3.92530…:Δu5=0.19452…
f(u4)=(−4.11982…)21+0.90044…(−4.11982…)20+0.81080…(−4.11982…)19+0.73008…(−4.11982…)18+0.65739…(−4.11982…)17+0.59195…(−4.11982…)16+0.53302…(−4.11982…)15+0.47995…(−4.11982…)14+0.43217…(−4.11982…)13+0.38914…(−4.11982…)12+0.35040…(−4.11982…)11+0.31552…(−4.11982…)10+0.28411…(−4.11982…)9+0.25582…(−4.11982…)8+0.23035…(−4.11982…)7+0.20742…(−4.11982…)6+0.18677…(−4.11982…)5+0.16818…(−4.11982…)4+0.15143…(−4.11982…)3+0.13636…(−4.11982…)2+0.12278…(−4.11982…)+1.11056…=−6708308285266.572f′(u4)=21(−4.11982…)20+18.00890…(−4.11982…)19+15.40523…(−4.11982…)18+13.14148…(−4.11982…)17+11.17579…(−4.11982…)16+9.47123…(−4.11982…)15+7.99531…(−4.11982…)14+6.71938…(−4.11982…)13+5.61826…(−4.11982…)12+4.66979…(−4.11982…)11+3.85448…(−4.11982…)10+3.15522…(−4.11982…)9+2.55699…(−4.11982…)8+2.04661…(−4.11982…)7+1.61250…(−4.11982…)6+1.24454…(−4.11982…)5+0.93387…(−4.11982…)4+0.67272…(−4.11982…)3+0.45431…(−4.11982…)2+0.27272…(−4.11982…)+0.12278…=3.44863E13u5=−3.92530…
Δu5=∣−3.92530…−(−4.11982…)∣=0.19452…Δu5=0.19452…
u6=−3.74003…:Δu6=0.18527…
f(u5)=(−3.92530…)21+0.90044…(−3.92530…)20+0.81080…(−3.92530…)19+0.73008…(−3.92530…)18+0.65739…(−3.92530…)17+0.59195…(−3.92530…)16+0.53302…(−3.92530…)15+0.47995…(−3.92530…)14+0.43217…(−3.92530…)13+0.38914…(−3.92530…)12+0.35040…(−3.92530…)11+0.31552…(−3.92530…)10+0.28411…(−3.92530…)9+0.25582…(−3.92530…)8+0.23035…(−3.92530…)7+0.20742…(−3.92530…)6+0.18677…(−3.92530…)5+0.16818…(−3.92530…)4+0.15143…(−3.92530…)3+0.13636…(−3.92530…)2+0.12278…(−3.92530…)+1.11056…=−2407995127242.657f′(u5)=21(−3.92530…)20+18.00890…(−3.92530…)19+15.40523…(−3.92530…)18+13.14148…(−3.92530…)17+11.17579…(−3.92530…)16+9.47123…(−3.92530…)15+7.99531…(−3.92530…)14+6.71938…(−3.92530…)13+5.61826…(−3.92530…)12+4.66979…(−3.92530…)11+3.85448…(−3.92530…)10+3.15522…(−3.92530…)9+2.55699…(−3.92530…)8+2.04661…(−3.92530…)7+1.61250…(−3.92530…)6+1.24454…(−3.92530…)5+0.93387…(−3.92530…)4+0.67272…(−3.92530…)3+0.45431…(−3.92530…)2+0.27272…(−3.92530…)+0.12278…=1.2997E13u6=−3.74003…
Δu6=∣−3.74003…−(−3.92530…)∣=0.18527…Δu6=0.18527…
u7=−3.56356…:Δu7=0.17646…
f(u6)=(−3.74003…)21+0.90044…(−3.74003…)20+0.81080…(−3.74003…)19+0.73008…(−3.74003…)18+0.65739…(−3.74003…)17+0.59195…(−3.74003…)16+0.53302…(−3.74003…)15+0.47995…(−3.74003…)14+0.43217…(−3.74003…)13+0.38914…(−3.74003…)12+0.35040…(−3.74003…)11+0.31552…(−3.74003…)10+0.28411…(−3.74003…)9+0.25582…(−3.74003…)8+0.23035…(−3.74003…)7+0.20742…(−3.74003…)6+0.18677…(−3.74003…)5+0.16818…(−3.74003…)4+0.15143…(−3.74003…)3+0.13636…(−3.74003…)2+0.12278…(−3.74003…)+1.11056…=−864369922719.6829f′(u6)=21(−3.74003…)20+18.00890…(−3.74003…)19+15.40523…(−3.74003…)18+13.14148…(−3.74003…)17+11.17579…(−3.74003…)16+9.47123…(−3.74003…)15+7.99531…(−3.74003…)14+6.71938…(−3.74003…)13+5.61826…(−3.74003…)12+4.66979…(−3.74003…)11+3.85448…(−3.74003…)10+3.15522…(−3.74003…)9+2.55699…(−3.74003…)8+2.04661…(−3.74003…)7+1.61250…(−3.74003…)6+1.24454…(−3.74003…)5+0.93387…(−3.74003…)4+0.67272…(−3.74003…)3+0.45431…(−3.74003…)2+0.27272…(−3.74003…)+0.12278…=4898215150703.34u7=−3.56356…
Δu7=∣−3.56356…−(−3.74003…)∣=0.17646…Δu7=0.17646…
u8=−3.39548…:Δu8=0.16807…
f(u7)=(−3.56356…)21+0.90044…(−3.56356…)20+0.81080…(−3.56356…)19+0.73008…(−3.56356…)18+0.65739…(−3.56356…)17+0.59195…(−3.56356…)16+0.53302…(−3.56356…)15+0.47995…(−3.56356…)14+0.43217…(−3.56356…)13+0.38914…(−3.56356…)12+0.35040…(−3.56356…)11+0.31552…(−3.56356…)10+0.28411…(−3.56356…)9+0.25582…(−3.56356…)8+0.23035…(−3.56356…)7+0.20742…(−3.56356…)6+0.18677…(−3.56356…)5+0.16818…(−3.56356…)4+0.15143…(−3.56356…)3+0.13636…(−3.56356…)2+0.12278…(−3.56356…)+1.11056…=−310273898602.6961f′(u7)=21(−3.56356…)20+18.00890…(−3.56356…)19+15.40523…(−3.56356…)18+13.14148…(−3.56356…)17+11.17579…(−3.56356…)16+9.47123…(−3.56356…)15+7.99531…(−3.56356…)14+6.71938…(−3.56356…)13+5.61826…(−3.56356…)12+4.66979…(−3.56356…)11+3.85448…(−3.56356…)10+3.15522…(−3.56356…)9+2.55699…(−3.56356…)8+2.04661…(−3.56356…)7+1.61250…(−3.56356…)6+1.24454…(−3.56356…)5+0.93387…(−3.56356…)4+0.67272…(−3.56356…)3+0.45431…(−3.56356…)2+0.27272…(−3.56356…)+0.12278…=1845997644672.9236u8=−3.39548…
Δu8=∣−3.39548…−(−3.56356…)∣=0.16807…Δu8=0.16807…
u9=−3.23539…:Δu9=0.16009…
f(u8)=(−3.39548…)21+0.90044…(−3.39548…)20+0.81080…(−3.39548…)19+0.73008…(−3.39548…)18+0.65739…(−3.39548…)17+0.59195…(−3.39548…)16+0.53302…(−3.39548…)15+0.47995…(−3.39548…)14+0.43217…(−3.39548…)13+0.38914…(−3.39548…)12+0.35040…(−3.39548…)11+0.31552…(−3.39548…)10+0.28411…(−3.39548…)9+0.25582…(−3.39548…)8+0.23035…(−3.39548…)7+0.20742…(−3.39548…)6+0.18677…(−3.39548…)5+0.16818…(−3.39548…)4+0.15143…(−3.39548…)3+0.13636…(−3.39548…)2+0.12278…(−3.39548…)+1.11056…=−111376226488.52354f′(u8)=21(−3.39548…)20+18.00890…(−3.39548…)19+15.40523…(−3.39548…)18+13.14148…(−3.39548…)17+11.17579…(−3.39548…)16+9.47123…(−3.39548…)15+7.99531…(−3.39548…)14+6.71938…(−3.39548…)13+5.61826…(−3.39548…)12+4.66979…(−3.39548…)11+3.85448…(−3.39548…)10+3.15522…(−3.39548…)9+2.55699…(−3.39548…)8+2.04661…(−3.39548…)7+1.61250…(−3.39548…)6+1.24454…(−3.39548…)5+0.93387…(−3.39548…)4+0.67272…(−3.39548…)3+0.45431…(−3.39548…)2+0.27272…(−3.39548…)+0.12278…=695701251270.6737u9=−3.23539…
Δu9=∣−3.23539…−(−3.39548…)∣=0.16009…Δu9=0.16009…
u10=−3.08291…:Δu10=0.15248…
f(u9)=(−3.23539…)21+0.90044…(−3.23539…)20+0.81080…(−3.23539…)19+0.73008…(−3.23539…)18+0.65739…(−3.23539…)17+0.59195…(−3.23539…)16+0.53302…(−3.23539…)15+0.47995…(−3.23539…)14+0.43217…(−3.23539…)13+0.38914…(−3.23539…)12+0.35040…(−3.23539…)11+0.31552…(−3.23539…)10+0.28411…(−3.23539…)9+0.25582…(−3.23539…)8+0.23035…(−3.23539…)7+0.20742…(−3.23539…)6+0.18677…(−3.23539…)5+0.16818…(−3.23539…)4+0.15143…(−3.23539…)3+0.13636…(−3.23539…)2+0.12278…(−3.23539…)+1.11056…=−39979883994.7629f′(u9)=21(−3.23539…)20+18.00890…(−3.23539…)19+15.40523…(−3.23539…)18+13.14148…(−3.23539…)17+11.17579…(−3.23539…)16+9.47123…(−3.23539…)15+7.99531…(−3.23539…)14+6.71938…(−3.23539…)13+5.61826…(−3.23539…)12+4.66979…(−3.23539…)11+3.85448…(−3.23539…)10+3.15522…(−3.23539…)9+2.55699…(−3.23539…)8+2.04661…(−3.23539…)7+1.61250…(−3.23539…)6+1.24454…(−3.23539…)5+0.93387…(−3.23539…)4+0.67272…(−3.23539…)3+0.45431…(−3.23539…)2+0.27272…(−3.23539…)+0.12278…=262187916511.76395u10=−3.08291…
Δu10=∣−3.08291…−(−3.23539…)∣=0.15248…Δu10=0.15248…
u11=−2.93766…:Δu11=0.14524…
f(u10)=(−3.08291…)21+0.90044…(−3.08291…)20+0.81080…(−3.08291…)19+0.73008…(−3.08291…)18+0.65739…(−3.08291…)17+0.59195…(−3.08291…)16+0.53302…(−3.08291…)15+0.47995…(−3.08291…)14+0.43217…(−3.08291…)13+0.38914…(−3.08291…)12+0.35040…(−3.08291…)11+0.31552…(−3.08291…)10+0.28411…(−3.08291…)9+0.25582…(−3.08291…)8+0.23035…(−3.08291…)7+0.20742…(−3.08291…)6+0.18677…(−3.08291…)5+0.16818…(−3.08291…)4+0.15143…(−3.08291…)3+0.13636…(−3.08291…)2+0.12278…(−3.08291…)+1.11056…=−14351339903.2129f′(u10)=21(−3.08291…)20+18.00890…(−3.08291…)19+15.40523…(−3.08291…)18+13.14148…(−3.08291…)17+11.17579…(−3.08291…)16+9.47123…(−3.08291…)15+7.99531…(−3.08291…)14+6.71938…(−3.08291…)13+5.61826…(−3.08291…)12+4.66979…(−3.08291…)11+3.85448…(−3.08291…)10+3.15522…(−3.08291…)9+2.55699…(−3.08291…)8+2.04661…(−3.08291…)7+1.61250…(−3.08291…)6+1.24454…(−3.08291…)5+0.93387…(−3.08291…)4+0.67272…(−3.08291…)3+0.45431…(−3.08291…)2+0.27272…(−3.08291…)+0.12278…=98809952554.07208u11=−2.93766…
Δu11=∣−2.93766…−(−3.08291…)∣=0.14524…Δu11=0.14524…
u12=−2.79932…:Δu12=0.13834…
f(u11)=(−2.93766…)21+0.90044…(−2.93766…)20+0.81080…(−2.93766…)19+0.73008…(−2.93766…)18+0.65739…(−2.93766…)17+0.59195…(−2.93766…)16+0.53302…(−2.93766…)15+0.47995…(−2.93766…)14+0.43217…(−2.93766…)13+0.38914…(−2.93766…)12+0.35040…(−2.93766…)11+0.31552…(−2.93766…)10+0.28411…(−2.93766…)9+0.25582…(−2.93766…)8+0.23035…(−2.93766…)7+0.20742…(−2.93766…)6+0.18677…(−2.93766…)5+0.16818…(−2.93766…)4+0.15143…(−2.93766…)3+0.13636…(−2.93766…)2+0.12278…(−2.93766…)+1.11056…=−5151638562.00959…f′(u11)=21(−2.93766…)20+18.00890…(−2.93766…)19+15.40523…(−2.93766…)18+13.14148…(−2.93766…)17+11.17579…(−2.93766…)16+9.47123…(−2.93766…)15+7.99531…(−2.93766…)14+6.71938…(−2.93766…)13+5.61826…(−2.93766…)12+4.66979…(−2.93766…)11+3.85448…(−2.93766…)10+3.15522…(−2.93766…)9+2.55699…(−2.93766…)8+2.04661…(−2.93766…)7+1.61250…(−2.93766…)6+1.24454…(−2.93766…)5+0.93387…(−2.93766…)4+0.67272…(−2.93766…)3+0.45431…(−2.93766…)2+0.27272…(−2.93766…)+0.12278…=37238031815.9361u12=−2.79932…
Δu12=∣−2.79932…−(−2.93766…)∣=0.13834…Δu12=0.13834…
u13=−2.66755…:Δu13=0.13177…
f(u12)=(−2.79932…)21+0.90044…(−2.79932…)20+0.81080…(−2.79932…)19+0.73008…(−2.79932…)18+0.65739…(−2.79932…)17+0.59195…(−2.79932…)16+0.53302…(−2.79932…)15+0.47995…(−2.79932…)14+0.43217…(−2.79932…)13+0.38914…(−2.79932…)12+0.35040…(−2.79932…)11+0.31552…(−2.79932…)10+0.28411…(−2.79932…)9+0.25582…(−2.79932…)8+0.23035…(−2.79932…)7+0.20742…(−2.79932…)6+0.18677…(−2.79932…)5+0.16818…(−2.79932…)4+0.15143…(−2.79932…)3+0.13636…(−2.79932…)2+0.12278…(−2.79932…)+1.11056…=−1849270587.78883…f′(u12)=21(−2.79932…)20+18.00890…(−2.79932…)19+15.40523…(−2.79932…)18+13.14148…(−2.79932…)17+11.17579…(−2.79932…)16+9.47123…(−2.79932…)15+7.99531…(−2.79932…)14+6.71938…(−2.79932…)13+5.61826…(−2.79932…)12+4.66979…(−2.79932…)11+3.85448…(−2.79932…)10+3.15522…(−2.79932…)9+2.55699…(−2.79932…)8+2.04661…(−2.79932…)7+1.61250…(−2.79932…)6+1.24454…(−2.79932…)5+0.93387…(−2.79932…)4+0.67272…(−2.79932…)3+0.45431…(−2.79932…)2+0.27272…(−2.79932…)+0.12278…=14033649653.68864u13=−2.66755…
Δu13=∣−2.66755…−(−2.79932…)∣=0.13177…Δu13=0.13177…
u14=−2.54203…:Δu14=0.12551…
f(u13)=(−2.66755…)21+0.90044…(−2.66755…)20+0.81080…(−2.66755…)19+0.73008…(−2.66755…)18+0.65739…(−2.66755…)17+0.59195…(−2.66755…)16+0.53302…(−2.66755…)15+0.47995…(−2.66755…)14+0.43217…(−2.66755…)13+0.38914…(−2.66755…)12+0.35040…(−2.66755…)11+0.31552…(−2.66755…)10+0.28411…(−2.66755…)9+0.25582…(−2.66755…)8+0.23035…(−2.66755…)7+0.20742…(−2.66755…)6+0.18677…(−2.66755…)5+0.16818…(−2.66755…)4+0.15143…(−2.66755…)3+0.13636…(−2.66755…)2+0.12278…(−2.66755…)+1.11056…=−663831436.16387…f′(u13)=21(−2.66755…)20+18.00890…(−2.66755…)19+15.40523…(−2.66755…)18+13.14148…(−2.66755…)17+11.17579…(−2.66755…)16+9.47123…(−2.66755…)15+7.99531…(−2.66755…)14+6.71938…(−2.66755…)13+5.61826…(−2.66755…)12+4.66979…(−2.66755…)11+3.85448…(−2.66755…)10+3.15522…(−2.66755…)9+2.55699…(−2.66755…)8+2.04661…(−2.66755…)7+1.61250…(−2.66755…)6+1.24454…(−2.66755…)5+0.93387…(−2.66755…)4+0.67272…(−2.66755…)3+0.45431…(−2.66755…)2+0.27272…(−2.66755…)+0.12278…=5288740946.36186u14=−2.54203…
Δu14=∣−2.54203…−(−2.66755…)∣=0.12551…Δu14=0.12551…
u15=−2.42247…:Δu15=0.11956…
f(u14)=(−2.54203…)21+0.90044…(−2.54203…)20+0.81080…(−2.54203…)19+0.73008…(−2.54203…)18+0.65739…(−2.54203…)17+0.59195…(−2.54203…)16+0.53302…(−2.54203…)15+0.47995…(−2.54203…)14+0.43217…(−2.54203…)13+0.38914…(−2.54203…)12+0.35040…(−2.54203…)11+0.31552…(−2.54203…)10+0.28411…(−2.54203…)9+0.25582…(−2.54203…)8+0.23035…(−2.54203…)7+0.20742…(−2.54203…)6+0.18677…(−2.54203…)5+0.16818…(−2.54203…)4+0.15143…(−2.54203…)3+0.13636…(−2.54203…)2+0.12278…(−2.54203…)+1.11056…=−238296454.73690…f′(u14)=21(−2.54203…)20+18.00890…(−2.54203…)19+15.40523…(−2.54203…)18+13.14148…(−2.54203…)17+11.17579…(−2.54203…)16+9.47123…(−2.54203…)15+7.99531…(−2.54203…)14+6.71938…(−2.54203…)13+5.61826…(−2.54203…)12+4.66979…(−2.54203…)11+3.85448…(−2.54203…)10+3.15522…(−2.54203…)9+2.55699…(−2.54203…)8+2.04661…(−2.54203…)7+1.61250…(−2.54203…)6+1.24454…(−2.54203…)5+0.93387…(−2.54203…)4+0.67272…(−2.54203…)3+0.45431…(−2.54203…)2+0.27272…(−2.54203…)+0.12278…=1993111417.62136…u15=−2.42247…
Δu15=∣−2.42247…−(−2.54203…)∣=0.11956…Δu15=0.11956…
u16=−2.30858…:Δu16=0.11388…
f(u15)=(−2.42247…)21+0.90044…(−2.42247…)20+0.81080…(−2.42247…)19+0.73008…(−2.42247…)18+0.65739…(−2.42247…)17+0.59195…(−2.42247…)16+0.53302…(−2.42247…)15+0.47995…(−2.42247…)14+0.43217…(−2.42247…)13+0.38914…(−2.42247…)12+0.35040…(−2.42247…)11+0.31552…(−2.42247…)10+0.28411…(−2.42247…)9+0.25582…(−2.42247…)8+0.23035…(−2.42247…)7+0.20742…(−2.42247…)6+0.18677…(−2.42247…)5+0.16818…(−2.42247…)4+0.15143…(−2.42247…)3+0.13636…(−2.42247…)2+0.12278…(−2.42247…)+1.11056…=−85542099.30396…f′(u15)=21(−2.42247…)20+18.00890…(−2.42247…)19+15.40523…(−2.42247…)18+13.14148…(−2.42247…)17+11.17579…(−2.42247…)16+9.47123…(−2.42247…)15+7.99531…(−2.42247…)14+6.71938…(−2.42247…)13+5.61826…(−2.42247…)12+4.66979…(−2.42247…)11+3.85448…(−2.42247…)10+3.15522…(−2.42247…)9+2.55699…(−2.42247…)8+2.04661…(−2.42247…)7+1.61250…(−2.42247…)6+1.24454…(−2.42247…)5+0.93387…(−2.42247…)4+0.67272…(−2.42247…)3+0.45431…(−2.42247…)2+0.27272…(−2.42247…)+0.12278…=751118289.55818…u16=−2.30858…
Δu16=∣−2.30858…−(−2.42247…)∣=0.11388…Δu16=0.11388…
u17=−2.20010…:Δu17=0.10848…
f(u16)=(−2.30858…)21+0.90044…(−2.30858…)20+0.81080…(−2.30858…)19+0.73008…(−2.30858…)18+0.65739…(−2.30858…)17+0.59195…(−2.30858…)16+0.53302…(−2.30858…)15+0.47995…(−2.30858…)14+0.43217…(−2.30858…)13+0.38914…(−2.30858…)12+0.35040…(−2.30858…)11+0.31552…(−2.30858…)10+0.28411…(−2.30858…)9+0.25582…(−2.30858…)8+0.23035…(−2.30858…)7+0.20742…(−2.30858…)6+0.18677…(−2.30858…)5+0.16818…(−2.30858…)4+0.15143…(−2.30858…)3+0.13636…(−2.30858…)2+0.12278…(−2.30858…)+1.11056…=−30707533.22041…f′(u16)=21(−2.30858…)20+18.00890…(−2.30858…)19+15.40523…(−2.30858…)18+13.14148…(−2.30858…)17+11.17579…(−2.30858…)16+9.47123…(−2.30858…)15+7.99531…(−2.30858…)14+6.71938…(−2.30858…)13+5.61826…(−2.30858…)12+4.66979…(−2.30858…)11+3.85448…(−2.30858…)10+3.15522…(−2.30858…)9+2.55699…(−2.30858…)8+2.04661…(−2.30858…)7+1.61250…(−2.30858…)6+1.24454…(−2.30858…)5+0.93387…(−2.30858…)4+0.67272…(−2.30858…)3+0.45431…(−2.30858…)2+0.27272…(−2.30858…)+0.12278…=283062561.44472…u17=−2.20010…
Δu17=∣−2.20010…−(−2.30858…)∣=0.10848…Δu17=0.10848…
u18=−2.09676…:Δu18=0.10333…
f(u17)=(−2.20010…)21+0.90044…(−2.20010…)20+0.81080…(−2.20010…)19+0.73008…(−2.20010…)18+0.65739…(−2.20010…)17+0.59195…(−2.20010…)16+0.53302…(−2.20010…)15+0.47995…(−2.20010…)14+0.43217…(−2.20010…)13+0.38914…(−2.20010…)12+0.35040…(−2.20010…)11+0.31552…(−2.20010…)10+0.28411…(−2.20010…)9+0.25582…(−2.20010…)8+0.23035…(−2.20010…)7+0.20742…(−2.20010…)6+0.18677…(−2.20010…)5+0.16818…(−2.20010…)4+0.15143…(−2.20010…)3+0.13636…(−2.20010…)2+0.12278…(−2.20010…)+1.11056…=−11023329.97685…f′(u17)=21(−2.20010…)20+18.00890…(−2.20010…)19+15.40523…(−2.20010…)18+13.14148…(−2.20010…)17+11.17579…(−2.20010…)16+9.47123…(−2.20010…)15+7.99531…(−2.20010…)14+6.71938…(−2.20010…)13+5.61826…(−2.20010…)12+4.66979…(−2.20010…)11+3.85448…(−2.20010…)10+3.15522…(−2.20010…)9+2.55699…(−2.20010…)8+2.04661…(−2.20010…)7+1.61250…(−2.20010…)6+1.24454…(−2.20010…)5+0.93387…(−2.20010…)4+0.67272…(−2.20010…)3+0.45431…(−2.20010…)2+0.27272…(−2.20010…)+0.12278…=106672806.07642…u18=−2.09676…
Δu18=∣−2.09676…−(−2.20010…)∣=0.10333…Δu18=0.10333…
u19=−1.99832…:Δu19=0.09843…
f(u18)=(−2.09676…)21+0.90044…(−2.09676…)20+0.81080…(−2.09676…)19+0.73008…(−2.09676…)18+0.65739…(−2.09676…)17+0.59195…(−2.09676…)16+0.53302…(−2.09676…)15+0.47995…(−2.09676…)14+0.43217…(−2.09676…)13+0.38914…(−2.09676…)12+0.35040…(−2.09676…)11+0.31552…(−2.09676…)10+0.28411…(−2.09676…)9+0.25582…(−2.09676…)8+0.23035…(−2.09676…)7+0.20742…(−2.09676…)6+0.18677…(−2.09676…)5+0.16818…(−2.09676…)4+0.15143…(−2.09676…)3+0.13636…(−2.09676…)2+0.12278…(−2.09676…)+1.11056…=−3957160.64645…f′(u18)=21(−2.09676…)20+18.00890…(−2.09676…)19+15.40523…(−2.09676…)18+13.14148…(−2.09676…)17+11.17579…(−2.09676…)16+9.47123…(−2.09676…)15+7.99531…(−2.09676…)14+6.71938…(−2.09676…)13+5.61826…(−2.09676…)12+4.66979…(−2.09676…)11+3.85448…(−2.09676…)10+3.15522…(−2.09676…)9+2.55699…(−2.09676…)8+2.04661…(−2.09676…)7+1.61250…(−2.09676…)6+1.24454…(−2.09676…)5+0.93387…(−2.09676…)4+0.67272…(−2.09676…)3+0.45431…(−2.09676…)2+0.27272…(−2.09676…)+0.12278…=40199630.61827…u19=−1.99832…
Δu19=∣−1.99832…−(−2.09676…)∣=0.09843…Δu19=0.09843…
u20=−1.90455…:Δu20=0.09377…
f(u19)=(−1.99832…)21+0.90044…(−1.99832…)20+0.81080…(−1.99832…)19+0.73008…(−1.99832…)18+0.65739…(−1.99832…)17+0.59195…(−1.99832…)16+0.53302…(−1.99832…)15+0.47995…(−1.99832…)14+0.43217…(−1.99832…)13+0.38914…(−1.99832…)12+0.35040…(−1.99832…)11+0.31552…(−1.99832…)10+0.28411…(−1.99832…)9+0.25582…(−1.99832…)8+0.23035…(−1.99832…)7+0.20742…(−1.99832…)6+0.18677…(−1.99832…)5+0.16818…(−1.99832…)4+0.15143…(−1.99832…)3+0.13636…(−1.99832…)2+0.12278…(−1.99832…)+1.11056…=−1420553.76977…f′(u19)=21(−1.99832…)20+18.00890…(−1.99832…)19+15.40523…(−1.99832…)18+13.14148…(−1.99832…)17+11.17579…(−1.99832…)16+9.47123…(−1.99832…)15+7.99531…(−1.99832…)14+6.71938…(−1.99832…)13+5.61826…(−1.99832…)12+4.66979…(−1.99832…)11+3.85448…(−1.99832…)10+3.15522…(−1.99832…)9+2.55699…(−1.99832…)8+2.04661…(−1.99832…)7+1.61250…(−1.99832…)6+1.24454…(−1.99832…)5+0.93387…(−1.99832…)4+0.67272…(−1.99832…)3+0.45431…(−1.99832…)2+0.27272…(−1.99832…)+0.12278…=15149118.09714…u20=−1.90455…
Δu20=∣−1.90455…−(−1.99832…)∣=0.09377…Δu20=0.09377…
u21=−1.81522…:Δu21=0.08932…
f(u20)=(−1.90455…)21+0.90044…(−1.90455…)20+0.81080…(−1.90455…)19+0.73008…(−1.90455…)18+0.65739…(−1.90455…)17+0.59195…(−1.90455…)16+0.53302…(−1.90455…)15+0.47995…(−1.90455…)14+0.43217…(−1.90455…)13+0.38914…(−1.90455…)12+0.35040…(−1.90455…)11+0.31552…(−1.90455…)10+0.28411…(−1.90455…)9+0.25582…(−1.90455…)8+0.23035…(−1.90455…)7+0.20742…(−1.90455…)6+0.18677…(−1.90455…)5+0.16818…(−1.90455…)4+0.15143…(−1.90455…)3+0.13636…(−1.90455…)2+0.12278…(−1.90455…)+1.11056…=−509958.53262…f′(u20)=21(−1.90455…)20+18.00890…(−1.90455…)19+15.40523…(−1.90455…)18+13.14148…(−1.90455…)17+11.17579…(−1.90455…)16+9.47123…(−1.90455…)15+7.99531…(−1.90455…)14+6.71938…(−1.90455…)13+5.61826…(−1.90455…)12+4.66979…(−1.90455…)11+3.85448…(−1.90455…)10+3.15522…(−1.90455…)9+2.55699…(−1.90455…)8+2.04661…(−1.90455…)7+1.61250…(−1.90455…)6+1.24454…(−1.90455…)5+0.93387…(−1.90455…)4+0.67272…(−1.90455…)3+0.45431…(−1.90455…)2+0.27272…(−1.90455…)+0.12278…=5708862.14711…u21=−1.81522…
Δu21=∣−1.81522…−(−1.90455…)∣=0.08932…Δu21=0.08932…
u22=−1.73013…:Δu22=0.08509…
f(u21)=(−1.81522…)21+0.90044…(−1.81522…)20+0.81080…(−1.81522…)19+0.73008…(−1.81522…)18+0.65739…(−1.81522…)17+0.59195…(−1.81522…)16+0.53302…(−1.81522…)15+0.47995…(−1.81522…)14+0.43217…(−1.81522…)13+0.38914…(−1.81522…)12+0.35040…(−1.81522…)11+0.31552…(−1.81522…)10+0.28411…(−1.81522…)9+0.25582…(−1.81522…)8+0.23035…(−1.81522…)7+0.20742…(−1.81522…)6+0.18677…(−1.81522…)5+0.16818…(−1.81522…)4+0.15143…(−1.81522…)3+0.13636…(−1.81522…)2+0.12278…(−1.81522…)+1.11056…=−183069.13876…f′(u21)=21(−1.81522…)20+18.00890…(−1.81522…)19+15.40523…(−1.81522…)18+13.14148…(−1.81522…)17+11.17579…(−1.81522…)16+9.47123…(−1.81522…)15+7.99531…(−1.81522…)14+6.71938…(−1.81522…)13+5.61826…(−1.81522…)12+4.66979…(−1.81522…)11+3.85448…(−1.81522…)10+3.15522…(−1.81522…)9+2.55699…(−1.81522…)8+2.04661…(−1.81522…)7+1.61250…(−1.81522…)6+1.24454…(−1.81522…)5+0.93387…(−1.81522…)4+0.67272…(−1.81522…)3+0.45431…(−1.81522…)2+0.27272…(−1.81522…)+0.12278…=2151339.13938…u22=−1.73013…
Δu22=∣−1.73013…−(−1.81522…)∣=0.08509…Δu22=0.08509…
u23=−1.64906…:Δu23=0.08106…
f(u22)=(−1.73013…)21+0.90044…(−1.73013…)20+0.81080…(−1.73013…)19+0.73008…(−1.73013…)18+0.65739…(−1.73013…)17+0.59195…(−1.73013…)16+0.53302…(−1.73013…)15+0.47995…(−1.73013…)14+0.43217…(−1.73013…)13+0.38914…(−1.73013…)12+0.35040…(−1.73013…)11+0.31552…(−1.73013…)10+0.28411…(−1.73013…)9+0.25582…(−1.73013…)8+0.23035…(−1.73013…)7+0.20742…(−1.73013…)6+0.18677…(−1.73013…)5+0.16818…(−1.73013…)4+0.15143…(−1.73013…)3+0.13636…(−1.73013…)2+0.12278…(−1.73013…)+1.11056…=−65720.05634…f′(u22)=21(−1.73013…)20+18.00890…(−1.73013…)19+15.40523…(−1.73013…)18+13.14148…(−1.73013…)17+11.17579…(−1.73013…)16+9.47123…(−1.73013…)15+7.99531…(−1.73013…)14+6.71938…(−1.73013…)13+5.61826…(−1.73013…)12+4.66979…(−1.73013…)11+3.85448…(−1.73013…)10+3.15522…(−1.73013…)9+2.55699…(−1.73013…)8+2.04661…(−1.73013…)7+1.61250…(−1.73013…)6+1.24454…(−1.73013…)5+0.93387…(−1.73013…)4+0.67272…(−1.73013…)3+0.45431…(−1.73013…)2+0.27272…(−1.73013…)+0.12278…=810711.19059…u23=−1.64906…
Δu23=∣−1.64906…−(−1.73013…)∣=0.08106…Δu23=0.08106…
u24=−1.57184…:Δu24=0.07722…
f(u23)=(−1.64906…)21+0.90044…(−1.64906…)20+0.81080…(−1.64906…)19+0.73008…(−1.64906…)18+0.65739…(−1.64906…)17+0.59195…(−1.64906…)16+0.53302…(−1.64906…)15+0.47995…(−1.64906…)14+0.43217…(−1.64906…)13+0.38914…(−1.64906…)12+0.35040…(−1.64906…)11+0.31552…(−1.64906…)10+0.28411…(−1.64906…)9+0.25582…(−1.64906…)8+0.23035…(−1.64906…)7+0.20742…(−1.64906…)6+0.18677…(−1.64906…)5+0.16818…(−1.64906…)4+0.15143…(−1.64906…)3+0.13636…(−1.64906…)2+0.12278…(−1.64906…)+1.11056…=−23592.89955…f′(u23)=21(−1.64906…)20+18.00890…(−1.64906…)19+15.40523…(−1.64906…)18+13.14148…(−1.64906…)17+11.17579…(−1.64906…)16+9.47123…(−1.64906…)15+7.99531…(−1.64906…)14+6.71938…(−1.64906…)13+5.61826…(−1.64906…)12+4.66979…(−1.64906…)11+3.85448…(−1.64906…)10+3.15522…(−1.64906…)9+2.55699…(−1.64906…)8+2.04661…(−1.64906…)7+1.61250…(−1.64906…)6+1.24454…(−1.64906…)5+0.93387…(−1.64906…)4+0.67272…(−1.64906…)3+0.45431…(−1.64906…)2+0.27272…(−1.64906…)+0.12278…=305509.05572…u24=−1.57184…
Δu24=∣−1.57184…−(−1.64906…)∣=0.07722…Δu24=0.07722…
u25=−1.49828…:Δu25=0.07356…
f(u24)=(−1.57184…)21+0.90044…(−1.57184…)20+0.81080…(−1.57184…)19+0.73008…(−1.57184…)18+0.65739…(−1.57184…)17+0.59195…(−1.57184…)16+0.53302…(−1.57184…)15+0.47995…(−1.57184…)14+0.43217…(−1.57184…)13+0.38914…(−1.57184…)12+0.35040…(−1.57184…)11+0.31552…(−1.57184…)10+0.28411…(−1.57184…)9+0.25582…(−1.57184…)8+0.23035…(−1.57184…)7+0.20742…(−1.57184…)6+0.18677…(−1.57184…)5+0.16818…(−1.57184…)4+0.15143…(−1.57184…)3+0.13636…(−1.57184…)2+0.12278…(−1.57184…)+1.11056…=−8469.53719…f′(u24)=21(−1.57184…)20+18.00890…(−1.57184…)19+15.40523…(−1.57184…)18+13.14148…(−1.57184…)17+11.17579…(−1.57184…)16+9.47123…(−1.57184…)15+7.99531…(−1.57184…)14+6.71938…(−1.57184…)13+5.61826…(−1.57184…)12+4.66979…(−1.57184…)11+3.85448…(−1.57184…)10+3.15522…(−1.57184…)9+2.55699…(−1.57184…)8+2.04661…(−1.57184…)7+1.61250…(−1.57184…)6+1.24454…(−1.57184…)5+0.93387…(−1.57184…)4+0.67272…(−1.57184…)3+0.45431…(−1.57184…)2+0.27272…(−1.57184…)+0.12278…=115130.49303…u25=−1.49828…
Δu25=∣−1.49828…−(−1.57184…)∣=0.07356…Δu25=0.07356…
u26=−1.42821…:Δu26=0.07006…
f(u25)=(−1.49828…)21+0.90044…(−1.49828…)20+0.81080…(−1.49828…)19+0.73008…(−1.49828…)18+0.65739…(−1.49828…)17+0.59195…(−1.49828…)16+0.53302…(−1.49828…)15+0.47995…(−1.49828…)14+0.43217…(−1.49828…)13+0.38914…(−1.49828…)12+0.35040…(−1.49828…)11+0.31552…(−1.49828…)10+0.28411…(−1.49828…)9+0.25582…(−1.49828…)8+0.23035…(−1.49828…)7+0.20742…(−1.49828…)6+0.18677…(−1.49828…)5+0.16818…(−1.49828…)4+0.15143…(−1.49828…)3+0.13636…(−1.49828…)2+0.12278…(−1.49828…)+1.11056…=−3040.30385…f′(u25)=21(−1.49828…)20+18.00890…(−1.49828…)19+15.40523…(−1.49828…)18+13.14148…(−1.49828…)17+11.17579…(−1.49828…)16+9.47123…(−1.49828…)15+7.99531…(−1.49828…)14+6.71938…(−1.49828…)13+5.61826…(−1.49828…)12+4.66979…(−1.49828…)11+3.85448…(−1.49828…)10+3.15522…(−1.49828…)9+2.55699…(−1.49828…)8+2.04661…(−1.49828…)7+1.61250…(−1.49828…)6+1.24454…(−1.49828…)5+0.93387…(−1.49828…)4+0.67272…(−1.49828…)3+0.45431…(−1.49828…)2+0.27272…(−1.49828…)+0.12278…=43389.71952…u26=−1.42821…
Δu26=∣−1.42821…−(−1.49828…)∣=0.07006…Δu26=0.07006…
u27=−1.36149…:Δu27=0.06671…
f(u26)=(−1.42821…)21+0.90044…(−1.42821…)20+0.81080…(−1.42821…)19+0.73008…(−1.42821…)18+0.65739…(−1.42821…)17+0.59195…(−1.42821…)16+0.53302…(−1.42821…)15+0.47995…(−1.42821…)14+0.43217…(−1.42821…)13+0.38914…(−1.42821…)12+0.35040…(−1.42821…)11+0.31552…(−1.42821…)10+0.28411…(−1.42821…)9+0.25582…(−1.42821…)8+0.23035…(−1.42821…)7+0.20742…(−1.42821…)6+0.18677…(−1.42821…)5+0.16818…(−1.42821…)4+0.15143…(−1.42821…)3+0.13636…(−1.42821…)2+0.12278…(−1.42821…)+1.11056…=−1091.20979…f′(u26)=21(−1.42821…)20+18.00890…(−1.42821…)19+15.40523…(−1.42821…)18+13.14148…(−1.42821…)17+11.17579…(−1.42821…)16+9.47123…(−1.42821…)15+7.99531…(−1.42821…)14+6.71938…(−1.42821…)13+5.61826…(−1.42821…)12+4.66979…(−1.42821…)11+3.85448…(−1.42821…)10+3.15522…(−1.42821…)9+2.55699…(−1.42821…)8+2.04661…(−1.42821…)7+1.61250…(−1.42821…)6+1.24454…(−1.42821…)5+0.93387…(−1.42821…)4+0.67272…(−1.42821…)3+0.45431…(−1.42821…)2+0.27272…(−1.42821…)+0.12278…=16355.91082…u27=−1.36149…
Δu27=∣−1.36149…−(−1.42821…)∣=0.06671…Δu27=0.06671…
u28=−1.29803…:Δu28=0.06345…
f(u27)=(−1.36149…)21+0.90044…(−1.36149…)20+0.81080…(−1.36149…)19+0.73008…(−1.36149…)18+0.65739…(−1.36149…)17+0.59195…(−1.36149…)16+0.53302…(−1.36149…)15+0.47995…(−1.36149…)14+0.43217…(−1.36149…)13+0.38914…(−1.36149…)12+0.35040…(−1.36149…)11+0.31552…(−1.36149…)10+0.28411…(−1.36149…)9+0.25582…(−1.36149…)8+0.23035…(−1.36149…)7+0.20742…(−1.36149…)6+0.18677…(−1.36149…)5+0.16818…(−1.36149…)4+0.15143…(−1.36149…)3+0.13636…(−1.36149…)2+0.12278…(−1.36149…)+1.11056…=−391.47829…f′(u27)=21(−1.36149…)20+18.00890…(−1.36149…)19+15.40523…(−1.36149…)18+13.14148…(−1.36149…)17+11.17579…(−1.36149…)16+9.47123…(−1.36149…)15+7.99531…(−1.36149…)14+6.71938…(−1.36149…)13+5.61826…(−1.36149…)12+4.66979…(−1.36149…)11+3.85448…(−1.36149…)10+3.15522…(−1.36149…)9+2.55699…(−1.36149…)8+2.04661…(−1.36149…)7+1.61250…(−1.36149…)6+1.24454…(−1.36149…)5+0.93387…(−1.36149…)4+0.67272…(−1.36149…)3+0.45431…(−1.36149…)2+0.27272…(−1.36149…)+0.12278…=6169.14437…u28=−1.29803…
Δu28=∣−1.29803…−(−1.36149…)∣=0.06345…Δu28=0.06345…
u29=−1.23785…:Δu29=0.06017…
f(u28)=(−1.29803…)21+0.90044…(−1.29803…)20+0.81080…(−1.29803…)19+0.73008…(−1.29803…)18+0.65739…(−1.29803…)17+0.59195…(−1.29803…)16+0.53302…(−1.29803…)15+0.47995…(−1.29803…)14+0.43217…(−1.29803…)13+0.38914…(−1.29803…)12+0.35040…(−1.29803…)11+0.31552…(−1.29803…)10+0.28411…(−1.29803…)9+0.25582…(−1.29803…)8+0.23035…(−1.29803…)7+0.20742…(−1.29803…)6+0.18677…(−1.29803…)5+0.16818…(−1.29803…)4+0.15143…(−1.29803…)3+0.13636…(−1.29803…)2+0.12278…(−1.29803…)+1.11056…=−140.26975…f′(u28)=21(−1.29803…)20+18.00890…(−1.29803…)19+15.40523…(−1.29803…)18+13.14148…(−1.29803…)17+11.17579…(−1.29803…)16+9.47123…(−1.29803…)15+7.99531…(−1.29803…)14+6.71938…(−1.29803…)13+5.61826…(−1.29803…)12+4.66979…(−1.29803…)11+3.85448…(−1.29803…)10+3.15522…(−1.29803…)9+2.55699…(−1.29803…)8+2.04661…(−1.29803…)7+1.61250…(−1.29803…)6+1.24454…(−1.29803…)5+0.93387…(−1.29803…)4+0.67272…(−1.29803…)3+0.45431…(−1.29803…)2+0.27272…(−1.29803…)+0.12278…=2330.84515…u29=−1.23785…
Δu29=∣−1.23785…−(−1.29803…)∣=0.06017…Δu29=0.06017…
u30=−1.18125…:Δu30=0.05660…
f(u29)=(−1.23785…)21+0.90044…(−1.23785…)20+0.81080…(−1.23785…)19+0.73008…(−1.23785…)18+0.65739…(−1.23785…)17+0.59195…(−1.23785…)16+0.53302…(−1.23785…)15+0.47995…(−1.23785…)14+0.43217…(−1.23785…)13+0.38914…(−1.23785…)12+0.35040…(−1.23785…)11+0.31552…(−1.23785…)10+0.28411…(−1.23785…)9+0.25582…(−1.23785…)8+0.23035…(−1.23785…)7+0.20742…(−1.23785…)6+0.18677…(−1.23785…)5+0.16818…(−1.23785…)4+0.15143…(−1.23785…)3+0.13636…(−1.23785…)2+0.12278…(−1.23785…)+1.11056…=−50.08377…f′(u29)=21(−1.23785…)20+18.00890…(−1.23785…)19+15.40523…(−1.23785…)18+13.14148…(−1.23785…)17+11.17579…(−1.23785…)16+9.47123…(−1.23785…)15+7.99531…(−1.23785…)14+6.71938…(−1.23785…)13+5.61826…(−1.23785…)12+4.66979…(−1.23785…)11+3.85448…(−1.23785…)10+3.15522…(−1.23785…)9+2.55699…(−1.23785…)8+2.04661…(−1.23785…)7+1.61250…(−1.23785…)6+1.24454…(−1.23785…)5+0.93387…(−1.23785…)4+0.67272…(−1.23785…)3+0.45431…(−1.23785…)2+0.27272…(−1.23785…)+0.12278…=884.83186…u30=−1.18125…
Δu30=∣−1.18125…−(−1.23785…)∣=0.05660…Δu30=0.05660…
u31=−1.12922…:Δu31=0.05203…
f(u30)=(−1.18125…)21+0.90044…(−1.18125…)20+0.81080…(−1.18125…)19+0.73008…(−1.18125…)18+0.65739…(−1.18125…)17+0.59195…(−1.18125…)16+0.53302…(−1.18125…)15+0.47995…(−1.18125…)14+0.43217…(−1.18125…)13+0.38914…(−1.18125…)12+0.35040…(−1.18125…)11+0.31552…(−1.18125…)10+0.28411…(−1.18125…)9+0.25582…(−1.18125…)8+0.23035…(−1.18125…)7+0.20742…(−1.18125…)6+0.18677…(−1.18125…)5+0.16818…(−1.18125…)4+0.15143…(−1.18125…)3+0.13636…(−1.18125…)2+0.12278…(−1.18125…)+1.11056…=−17.70794…f′(u30)=21(−1.18125…)20+18.00890…(−1.18125…)19+15.40523…(−1.18125…)18+13.14148…(−1.18125…)17+11.17579…(−1.18125…)16+9.47123…(−1.18125…)15+7.99531…(−1.18125…)14+6.71938…(−1.18125…)13+5.61826…(−1.18125…)12+4.66979…(−1.18125…)11+3.85448…(−1.18125…)10+3.15522…(−1.18125…)9+2.55699…(−1.18125…)8+2.04661…(−1.18125…)7+1.61250…(−1.18125…)6+1.24454…(−1.18125…)5+0.93387…(−1.18125…)4+0.67272…(−1.18125…)3+0.45431…(−1.18125…)2+0.27272…(−1.18125…)+0.12278…=340.32564…u31=−1.12922…
Δu31=∣−1.12922…−(−1.18125…)∣=0.05203…Δu31=0.05203…
u32=−1.08430…:Δu32=0.04491…
f(u31)=(−1.12922…)21+0.90044…(−1.12922…)20+0.81080…(−1.12922…)19+0.73008…(−1.12922…)18+0.65739…(−1.12922…)17+0.59195…(−1.12922…)16+0.53302…(−1.12922…)15+0.47995…(−1.12922…)14+0.43217…(−1.12922…)13+0.38914…(−1.12922…)12+0.35040…(−1.12922…)11+0.31552…(−1.12922…)10+0.28411…(−1.12922…)9+0.25582…(−1.12922…)8+0.23035…(−1.12922…)7+0.20742…(−1.12922…)6+0.18677…(−1.12922…)5+0.16818…(−1.12922…)4+0.15143…(−1.12922…)3+0.13636…(−1.12922…)2+0.12278…(−1.12922…)+1.11056…=−6.09127…f′(u31)=21(−1.12922…)20+18.00890…(−1.12922…)19+15.40523…(−1.12922…)18+13.14148…(−1.12922…)17+11.17579…(−1.12922…)16+9.47123…(−1.12922…)15+7.99531…(−1.12922…)14+6.71938…(−1.12922…)13+5.61826…(−1.12922…)12+4.66979…(−1.12922…)11+3.85448…(−1.12922…)10+3.15522…(−1.12922…)9+2.55699…(−1.12922…)8+2.04661…(−1.12922…)7+1.61250…(−1.12922…)6+1.24454…(−1.12922…)5+0.93387…(−1.12922…)4+0.67272…(−1.12922…)3+0.45431…(−1.12922…)2+0.27272…(−1.12922…)+0.12278…=135.61716…u32=−1.08430…
Δu32=∣−1.08430…−(−1.12922…)∣=0.04491…Δu32=0.04491…
u33=−1.05153…:Δu33=0.03277…
f(u32)=(−1.08430…)21+0.90044…(−1.08430…)20+0.81080…(−1.08430…)19+0.73008…(−1.08430…)18+0.65739…(−1.08430…)17+0.59195…(−1.08430…)16+0.53302…(−1.08430…)15+0.47995…(−1.08430…)14+0.43217…(−1.08430…)13+0.38914…(−1.08430…)12+0.35040…(−1.08430…)11+0.31552…(−1.08430…)10+0.28411…(−1.08430…)9+0.25582…(−1.08430…)8+0.23035…(−1.08430…)7+0.20742…(−1.08430…)6+0.18677…(−1.08430…)5+0.16818…(−1.08430…)4+0.15143…(−1.08430…)3+0.13636…(−1.08430…)2+0.12278…(−1.08430…)+1.11056…=−1.93961…f′(u32)=21(−1.08430…)20+18.00890…(−1.08430…)19+15.40523…(−1.08430…)18+13.14148…(−1.08430…)17+11.17579…(−1.08430…)16+9.47123…(−1.08430…)15+7.99531…(−1.08430…)14+6.71938…(−1.08430…)13+5.61826…(−1.08430…)12+4.66979…(−1.08430…)11+3.85448…(−1.08430…)10+3.15522…(−1.08430…)9+2.55699…(−1.08430…)8+2.04661…(−1.08430…)7+1.61250…(−1.08430…)6+1.24454…(−1.08430…)5+0.93387…(−1.08430…)4+0.67272…(−1.08430…)3+0.45431…(−1.08430…)2+0.27272…(−1.08430…)+0.12278…=59.17990…u33=−1.05153…
Δu33=∣−1.05153…−(−1.08430…)∣=0.03277…Δu33=0.03277…
u34=−1.03582…:Δu34=0.01570…
f(u33)=(−1.05153…)21+0.90044…(−1.05153…)20+0.81080…(−1.05153…)19+0.73008…(−1.05153…)18+0.65739…(−1.05153…)17+0.59195…(−1.05153…)16+0.53302…(−1.05153…)15+0.47995…(−1.05153…)14+0.43217…(−1.05153…)13+0.38914…(−1.05153…)12+0.35040…(−1.05153…)11+0.31552…(−1.05153…)10+0.28411…(−1.05153…)9+0.25582…(−1.05153…)8+0.23035…(−1.05153…)7+0.20742…(−1.05153…)6+0.18677…(−1.05153…)5+0.16818…(−1.05153…)4+0.15143…(−1.05153…)3+0.13636…(−1.05153…)2+0.12278…(−1.05153…)+1.11056…=−0.49644…f′(u33)=21(−1.05153…)20+18.00890…(−1.05153…)19+15.40523…(−1.05153…)18+13.14148…(−1.05153…)17+11.17579…(−1.05153…)16+9.47123…(−1.05153…)15+7.99531…(−1.05153…)14+6.71938…(−1.05153…)13+5.61826…(−1.05153…)12+4.66979…(−1.05153…)11+3.85448…(−1.05153…)10+3.15522…(−1.05153…)9+2.55699…(−1.05153…)8+2.04661…(−1.05153…)7+1.61250…(−1.05153…)6+1.24454…(−1.05153…)5+0.93387…(−1.05153…)4+0.67272…(−1.05153…)3+0.45431…(−1.05153…)2+0.27272…(−1.05153…)+0.12278…=31.60885…u34=−1.03582…
Δu34=∣−1.03582…−(−1.05153…)∣=0.01570…Δu34=0.01570…
u35=−1.03286…:Δu35=0.00296…
f(u34)=(−1.03582…)21+0.90044…(−1.03582…)20+0.81080…(−1.03582…)19+0.73008…(−1.03582…)18+0.65739…(−1.03582…)17+0.59195…(−1.03582…)16+0.53302…(−1.03582…)15+0.47995…(−1.03582…)14+0.43217…(−1.03582…)13+0.38914…(−1.03582…)12+0.35040…(−1.03582…)11+0.31552…(−1.03582…)10+0.28411…(−1.03582…)9+0.25582…(−1.03582…)8+0.23035…(−1.03582…)7+0.20742…(−1.03582…)6+0.18677…(−1.03582…)5+0.16818…(−1.03582…)4+0.15143…(−1.03582…)3+0.13636…(−1.03582…)2+0.12278…(−1.03582…)+1.11056…=−0.06889…f′(u34)=21(−1.03582…)20+18.00890…(−1.03582…)19+15.40523…(−1.03582…)18+13.14148…(−1.03582…)17+11.17579…(−1.03582…)16+9.47123…(−1.03582…)15+7.99531…(−1.03582…)14+6.71938…(−1.03582…)13+5.61826…(−1.03582…)12+4.66979…(−1.03582…)11+3.85448…(−1.03582…)10+3.15522…(−1.03582…)9+2.55699…(−1.03582…)8+2.04661…(−1.03582…)7+1.61250…(−1.03582…)6+1.24454…(−1.03582…)5+0.93387…(−1.03582…)4+0.67272…(−1.03582…)3+0.45431…(−1.03582…)2+0.27272…(−1.03582…)+0.12278…=23.24244…u35=−1.03286…
Δu35=∣−1.03286…−(−1.03582…)∣=0.00296…Δu35=0.00296…
u36=−1.03277…:Δu36=0.00009…
f(u35)=(−1.03286…)21+0.90044…(−1.03286…)20+0.81080…(−1.03286…)19+0.73008…(−1.03286…)18+0.65739…(−1.03286…)17+0.59195…(−1.03286…)16+0.53302…(−1.03286…)15+0.47995…(−1.03286…)14+0.43217…(−1.03286…)13+0.38914…(−1.03286…)12+0.35040…(−1.03286…)11+0.31552…(−1.03286…)10+0.28411…(−1.03286…)9+0.25582…(−1.03286…)8+0.23035…(−1.03286…)7+0.20742…(−1.03286…)6+0.18677…(−1.03286…)5+0.16818…(−1.03286…)4+0.15143…(−1.03286…)3+0.13636…(−1.03286…)2+0.12278…(−1.03286…)+1.11056…=−0.00197…f′(u35)=21(−1.03286…)20+18.00890…(−1.03286…)19+15.40523…(−1.03286…)18+13.14148…(−1.03286…)17+11.17579…(−1.03286…)16+9.47123…(−1.03286…)15+7.99531…(−1.03286…)14+6.71938…(−1.03286…)13+5.61826…(−1.03286…)12+4.66979…(−1.03286…)11+3.85448…(−1.03286…)10+3.15522…(−1.03286…)9+2.55699…(−1.03286…)8+2.04661…(−1.03286…)7+1.61250…(−1.03286…)6+1.24454…(−1.03286…)5+0.93387…(−1.03286…)4+0.67272…(−1.03286…)3+0.45431…(−1.03286…)2+0.27272…(−1.03286…)+0.12278…=21.92073…u36=−1.03277…
Δu36=∣−1.03277…−(−1.03286…)∣=0.00009…Δu36=0.00009…
u37=−1.03277…:Δu37=8.05532E−8
f(u36)=(−1.03277…)21+0.90044…(−1.03277…)20+0.81080…(−1.03277…)19+0.73008…(−1.03277…)18+0.65739…(−1.03277…)17+0.59195…(−1.03277…)16+0.53302…(−1.03277…)15+0.47995…(−1.03277…)14+0.43217…(−1.03277…)13+0.38914…(−1.03277…)12+0.35040…(−1.03277…)11+0.31552…(−1.03277…)10+0.28411…(−1.03277…)9+0.25582…(−1.03277…)8+0.23035…(−1.03277…)7+0.20742…(−1.03277…)6+0.18677…(−1.03277…)5+0.16818…(−1.03277…)4+0.15143…(−1.03277…)3+0.13636…(−1.03277…)2+0.12278…(−1.03277…)+1.11056…=−1.76264E−6f′(u36)=21(−1.03277…)20+18.00890…(−1.03277…)19+15.40523…(−1.03277…)18+13.14148…(−1.03277…)17+11.17579…(−1.03277…)16+9.47123…(−1.03277…)15+7.99531…(−1.03277…)14+6.71938…(−1.03277…)13+5.61826…(−1.03277…)12+4.66979…(−1.03277…)11+3.85448…(−1.03277…)10+3.15522…(−1.03277…)9+2.55699…(−1.03277…)8+2.04661…(−1.03277…)7+1.61250…(−1.03277…)6+1.24454…(−1.03277…)5+0.93387…(−1.03277…)4+0.67272…(−1.03277…)3+0.45431…(−1.03277…)2+0.27272…(−1.03277…)+0.12278…=21.88166…u37=−1.03277…
Δu37=∣−1.03277…−(−1.03277…)∣=8.05532E−8Δu37=8.05532E−8
u≈−1.03277…
Aplicar la división larga Equation0:u+1.03277…u21+0.90044…u20+0.81080…u19+0.73008…u18+0.65739…u17+0.59195…u16+0.53302…u15+0.47995…u14+0.43217…u13+0.38914…u12+0.35040…u11+0.31552…u10+0.28411…u9+0.25582…u8+0.23035…u7+0.20742…u6+0.18677…u5+0.16818…u4+0.15143…u3+0.13636…u2+0.12278…u+1.11056…=u20−0.13232…u19+0.94746…u18−0.24843…u17+0.91397…u16−0.35197…u15+0.89652…u14−0.44594…u13+0.89273…u12−0.53284…u11+0.90071…u10−0.61470…u9+0.91896…u8−0.69325…u7+0.94632…u6−0.76991…u5+0.98192…u4−0.84592…u3+1.02507…u2−0.92231…u+1.07532…
u20−0.13232…u19+0.94746…u18−0.24843…u17+0.91397…u16−0.35197…u15+0.89652…u14−0.44594…u13+0.89273…u12−0.53284…u11+0.90071…u10−0.61470…u9+0.91896…u8−0.69325…u7+0.94632…u6−0.76991…u5+0.98192…u4−0.84592…u3+1.02507…u2−0.92231…u+1.07532…≈0
Encontrar una solución para u20−0.13232…u19+0.94746…u18−0.24843…u17+0.91397…u16−0.35197…u15+0.89652…u14−0.44594…u13+0.89273…u12−0.53284…u11+0.90071…u10−0.61470…u9+0.91896…u8−0.69325…u7+0.94632…u6−0.76991…u5+0.98192…u4−0.84592…u3+1.02507…u2−0.92231…u+1.07532…=0 utilizando el método de Newton-Raphson:Sin solución para u∈R
u20−0.13232…u19+0.94746…u18−0.24843…u17+0.91397…u16−0.35197…u15+0.89652…u14−0.44594…u13+0.89273…u12−0.53284…u11+0.90071…u10−0.61470…u9+0.91896…u8−0.69325…u7+0.94632…u6−0.76991…u5+0.98192…u4−0.84592…u3+1.02507…u2−0.92231…u+1.07532…=0
Definición del método de Newton-Raphson
f(u)=u20−0.13232…u19+0.94746…u18−0.24843…u17+0.91397…u16−0.35197…u15+0.89652…u14−0.44594…u13+0.89273…u12−0.53284…u11+0.90071…u10−0.61470…u9+0.91896…u8−0.69325…u7+0.94632…u6−0.76991…u5+0.98192…u4−0.84592…u3+1.02507…u2−0.92231…u+1.07532…
Hallar f′(u):20u19−2.51418…u18+17.05434…u17−4.22331…u16+14.62354…u15−5.27956…u14+12.55136…u13−5.79734…u12+10.71285…u11−5.86129…u10+9.00714…u9−5.53237…u8+7.35171…u7−4.85277…u6+5.67797…u5−3.84958…u4+3.92769…u3−2.53776…u2+2.05015…u−0.92231…
Sea u0=1Calcular un+1 hasta que Δun+1<0.000001
u1=0.91976…:Δu1=0.08023…
f(u0)=120−0.13232…⋅119+0.94746…⋅118−0.24843…⋅117+0.91397…⋅116−0.35197…⋅115+0.89652…⋅114−0.44594…⋅113+0.89273…⋅112−0.53284…⋅111+0.90071…⋅110−0.61470…⋅19+0.91896…⋅18−0.69325…⋅17+0.94632…⋅16−0.76991…⋅15+0.98192…⋅14−0.84592…⋅13+1.02507…⋅12−0.92231…⋅1+1.07532…=4.94139…f′(u0)=20⋅119−2.51418…⋅118+17.05434…⋅117−4.22331…⋅116+14.62354…⋅115−5.27956…⋅114+12.55136…⋅113−5.79734…⋅112+10.71285…⋅111−5.86129…⋅110+9.00714…⋅19−5.53237…⋅18+7.35171…⋅17−4.85277…⋅16+5.67797…⋅15−3.84958…⋅14+3.92769…⋅13−2.53776…⋅12+2.05015…⋅1−0.92231…=61.58627…u1=0.91976…
Δu1=∣0.91976…−1∣=0.08023…Δu1=0.08023…
u2=0.80606…:Δu2=0.11369…
f(u1)=0.91976…20−0.13232…⋅0.91976…19+0.94746…⋅0.91976…18−0.24843…⋅0.91976…17+0.91397…⋅0.91976…16−0.35197…⋅0.91976…15+0.89652…⋅0.91976…14−0.44594…⋅0.91976…13+0.89273…⋅0.91976…12−0.53284…⋅0.91976…11+0.90071…⋅0.91976…10−0.61470…⋅0.91976…9+0.91896…⋅0.91976…8−0.69325…⋅0.91976…7+0.94632…⋅0.91976…6−0.76991…⋅0.91976…5+0.98192…⋅0.91976…4−0.84592…⋅0.91976…3+1.02507…⋅0.91976…2−0.92231…⋅0.91976…+1.07532…=2.08310…f′(u1)=20⋅0.91976…19−2.51418…⋅0.91976…18+17.05434…⋅0.91976…17−4.22331…⋅0.91976…16+14.62354…⋅0.91976…15−5.27956…⋅0.91976…14+12.55136…⋅0.91976…13−5.79734…⋅0.91976…12+10.71285…⋅0.91976…11−5.86129…⋅0.91976…10+9.00714…⋅0.91976…9−5.53237…⋅0.91976…8+7.35171…⋅0.91976…7−4.85277…⋅0.91976…6+5.67797…⋅0.91976…5−3.84958…⋅0.91976…4+3.92769…⋅0.91976…3−2.53776…⋅0.91976…2+2.05015…⋅0.91976…−0.92231…=18.32114…u2=0.80606…
Δu2=∣0.80606…−0.91976…∣=0.11369…Δu2=0.11369…
u3=0.50923…:Δu3=0.29683…
f(u2)=0.80606…20−0.13232…⋅0.80606…19+0.94746…⋅0.80606…18−0.24843…⋅0.80606…17+0.91397…⋅0.80606…16−0.35197…⋅0.80606…15+0.89652…⋅0.80606…14−0.44594…⋅0.80606…13+0.89273…⋅0.80606…12−0.53284…⋅0.80606…11+0.90071…⋅0.80606…10−0.61470…⋅0.80606…9+0.91896…⋅0.80606…8−0.69325…⋅0.80606…7+0.94632…⋅0.80606…6−0.76991…⋅0.80606…5+0.98192…⋅0.80606…4−0.84592…⋅0.80606…3+1.02507…⋅0.80606…2−0.92231…⋅0.80606…+1.07532…=1.06725…f′(u2)=20⋅0.80606…19−2.51418…⋅0.80606…18+17.05434…⋅0.80606…17−4.22331…⋅0.80606…16+14.62354…⋅0.80606…15−5.27956…⋅0.80606…14+12.55136…⋅0.80606…13−5.79734…⋅0.80606…12+10.71285…⋅0.80606…11−5.86129…⋅0.80606…10+9.00714…⋅0.80606…9−5.53237…⋅0.80606…8+7.35171…⋅0.80606…7−4.85277…⋅0.80606…6+5.67797…⋅0.80606…5−3.84958…⋅0.80606…4+3.92769…⋅0.80606…3−2.53776…⋅0.80606…2+2.05015…⋅0.80606…−0.92231…=3.59547…u3=0.50923…
Δu3=∣0.50923…−0.80606…∣=0.29683…Δu3=0.29683…
u4=8.20066…:Δu4=7.69143…
f(u3)=0.50923…20−0.13232…⋅0.50923…19+0.94746…⋅0.50923…18−0.24843…⋅0.50923…17+0.91397…⋅0.50923…16−0.35197…⋅0.50923…15+0.89652…⋅0.50923…14−0.44594…⋅0.50923…13+0.89273…⋅0.50923…12−0.53284…⋅0.50923…11+0.90071…⋅0.50923…10−0.61470…⋅0.50923…9+0.91896…⋅0.50923…8−0.69325…⋅0.50923…7+0.94632…⋅0.50923…6−0.76991…⋅0.50923…5+0.98192…⋅0.50923…4−0.84592…⋅0.50923…3+1.02507…⋅0.50923…2−0.92231…⋅0.50923…+1.07532…=0.81353…f′(u3)=20⋅0.50923…19−2.51418…⋅0.50923…18+17.05434…⋅0.50923…17−4.22331…⋅0.50923…16+14.62354…⋅0.50923…15−5.27956…⋅0.50923…14+12.55136…⋅0.50923…13−5.79734…⋅0.50923…12+10.71285…⋅0.50923…11−5.86129…⋅0.50923…10+9.00714…⋅0.50923…9−5.53237…⋅0.50923…8+7.35171…⋅0.50923…7−4.85277…⋅0.50923…6+5.67797…⋅0.50923…5−3.84958…⋅0.50923…4+3.92769…⋅0.50923…3−2.53776…⋅0.50923…2+2.05015…⋅0.50923…−0.92231…=−0.10577…u4=8.20066…
Δu4=∣8.20066…−0.50923…∣=7.69143…Δu4=7.69143…
u5=7.79039…:Δu5=0.41026…
f(u4)=8.20066…20−0.13232…⋅8.20066…19+0.94746…⋅8.20066…18−0.24843…⋅8.20066…17+0.91397…⋅8.20066…16−0.35197…⋅8.20066…15+0.89652…⋅8.20066…14−0.44594…⋅8.20066…13+0.89273…⋅8.20066…12−0.53284…⋅8.20066…11+0.90071…⋅8.20066…10−0.61470…⋅8.20066…9+0.91896…⋅8.20066…8−0.69325…⋅8.20066…7+0.94632…⋅8.20066…6−0.76991…⋅8.20066…5+0.98192…⋅8.20066…4−0.84592…⋅8.20066…3+1.02507…⋅8.20066…2−0.92231…⋅8.20066…+1.07532…=1.8879E18f′(u4)=20⋅8.20066…19−2.51418…⋅8.20066…18+17.05434…⋅8.20066…17−4.22331…⋅8.20066…16+14.62354…⋅8.20066…15−5.27956…⋅8.20066…14+12.55136…⋅8.20066…13−5.79734…⋅8.20066…12+10.71285…⋅8.20066…11−5.86129…⋅8.20066…10+9.00714…⋅8.20066…9−5.53237…⋅8.20066…8+7.35171…⋅8.20066…7−4.85277…⋅8.20066…6+5.67797…⋅8.20066…5−3.84958…⋅8.20066…4+3.92769…⋅8.20066…3−2.53776…⋅8.20066…2+2.05015…⋅8.20066…−0.92231…=4.60163E18u5=7.79039…
Δu5=∣7.79039…−8.20066…∣=0.41026…Δu5=0.41026…
u6=7.40061…:Δu6=0.38978…
f(u5)=7.79039…20−0.13232…⋅7.79039…19+0.94746…⋅7.79039…18−0.24843…⋅7.79039…17+0.91397…⋅7.79039…16−0.35197…⋅7.79039…15+0.89652…⋅7.79039…14−0.44594…⋅7.79039…13+0.89273…⋅7.79039…12−0.53284…⋅7.79039…11+0.90071…⋅7.79039…10−0.61470…⋅7.79039…9+0.91896…⋅7.79039…8−0.69325…⋅7.79039…7+0.94632…⋅7.79039…6−0.76991…⋅7.79039…5+0.98192…⋅7.79039…4−0.84592…⋅7.79039…3+1.02507…⋅7.79039…2−0.92231…⋅7.79039…+1.07532…=6.76813E17f′(u5)=20⋅7.79039…19−2.51418…⋅7.79039…18+17.05434…⋅7.79039…17−4.22331…⋅7.79039…16+14.62354…⋅7.79039…15−5.27956…⋅7.79039…14+12.55136…⋅7.79039…13−5.79734…⋅7.79039…12+10.71285…⋅7.79039…11−5.86129…⋅7.79039…10+9.00714…⋅7.79039…9−5.53237…⋅7.79039…8+7.35171…⋅7.79039…7−4.85277…⋅7.79039…6+5.67797…⋅7.79039…5−3.84958…⋅7.79039…4+3.92769…⋅7.79039…3−2.53776…⋅7.79039…2+2.05015…⋅7.79039…−0.92231…=1.73637E18u6=7.40061…
Δu6=∣7.40061…−7.79039…∣=0.38978…Δu6=0.38978…
u7=7.03028…:Δu7=0.37032…
f(u6)=7.40061…20−0.13232…⋅7.40061…19+0.94746…⋅7.40061…18−0.24843…⋅7.40061…17+0.91397…⋅7.40061…16−0.35197…⋅7.40061…15+0.89652…⋅7.40061…14−0.44594…⋅7.40061…13+0.89273…⋅7.40061…12−0.53284…⋅7.40061…11+0.90071…⋅7.40061…10−0.61470…⋅7.40061…9+0.91896…⋅7.40061…8−0.69325…⋅7.40061…7+0.94632…⋅7.40061…6−0.76991…⋅7.40061…5+0.98192…⋅7.40061…4−0.84592…⋅7.40061…3+1.02507…⋅7.40061…2−0.92231…⋅7.40061…+1.07532…=2.42638E17f′(u6)=20⋅7.40061…19−2.51418…⋅7.40061…18+17.05434…⋅7.40061…17−4.22331…⋅7.40061…16+14.62354…⋅7.40061…15−5.27956…⋅7.40061…14+12.55136…⋅7.40061…13−5.79734…⋅7.40061…12+10.71285…⋅7.40061…11−5.86129…⋅7.40061…10+9.00714…⋅7.40061…9−5.53237…⋅7.40061…8+7.35171…⋅7.40061…7−4.85277…⋅7.40061…6+5.67797…⋅7.40061…5−3.84958…⋅7.40061…4+3.92769…⋅7.40061…3−2.53776…⋅7.40061…2+2.05015…⋅7.40061…−0.92231…=6.55199E17u7=7.03028…
Δu7=∣7.03028…−7.40061…∣=0.37032…Δu7=0.37032…
u8=6.67843…:Δu8=0.35184…
f(u7)=7.03028…20−0.13232…⋅7.03028…19+0.94746…⋅7.03028…18−0.24843…⋅7.03028…17+0.91397…⋅7.03028…16−0.35197…⋅7.03028…15+0.89652…⋅7.03028…14−0.44594…⋅7.03028…13+0.89273…⋅7.03028…12−0.53284…⋅7.03028…11+0.90071…⋅7.03028…10−0.61470…⋅7.03028…9+0.91896…⋅7.03028…8−0.69325…⋅7.03028…7+0.94632…⋅7.03028…6−0.76991…⋅7.03028…5+0.98192…⋅7.03028…4−0.84592…⋅7.03028…3+1.02507…⋅7.03028…2−0.92231…⋅7.03028…+1.07532…=8.69866E16f′(u7)=20⋅7.03028…19−2.51418…⋅7.03028…18+17.05434…⋅7.03028…17−4.22331…⋅7.03028…16+14.62354…⋅7.03028…15−5.27956…⋅7.03028…14+12.55136…⋅7.03028…13−5.79734…⋅7.03028…12+10.71285…⋅7.03028…11−5.86129…⋅7.03028…10+9.00714…⋅7.03028…9−5.53237…⋅7.03028…8+7.35171…⋅7.03028…7−4.85277…⋅7.03028…6+5.67797…⋅7.03028…5−3.84958…⋅7.03028…4+3.92769…⋅7.03028…3−2.53776…⋅7.03028…2+2.05015…⋅7.03028…−0.92231…=2.4723E17u8=6.67843…
Δu8=∣6.67843…−7.03028…∣=0.35184…Δu8=0.35184…
u9=6.34414…:Δu9=0.33428…
f(u8)=6.67843…20−0.13232…⋅6.67843…19+0.94746…⋅6.67843…18−0.24843…⋅6.67843…17+0.91397…⋅6.67843…16−0.35197…⋅6.67843…15+0.89652…⋅6.67843…14−0.44594…⋅6.67843…13+0.89273…⋅6.67843…12−0.53284…⋅6.67843…11+0.90071…⋅6.67843…10−0.61470…⋅6.67843…9+0.91896…⋅6.67843…8−0.69325…⋅6.67843…7+0.94632…⋅6.67843…6−0.76991…⋅6.67843…5+0.98192…⋅6.67843…4−0.84592…⋅6.67843…3+1.02507…⋅6.67843…2−0.92231…⋅6.67843…+1.07532…=3.11851E16f′(u8)=20⋅6.67843…19−2.51418…⋅6.67843…18+17.05434…⋅6.67843…17−4.22331…⋅6.67843…16+14.62354…⋅6.67843…15−5.27956…⋅6.67843…14+12.55136…⋅6.67843…13−5.79734…⋅6.67843…12+10.71285…⋅6.67843…11−5.86129…⋅6.67843…10+9.00714…⋅6.67843…9−5.53237…⋅6.67843…8+7.35171…⋅6.67843…7−4.85277…⋅6.67843…6+5.67797…⋅6.67843…5−3.84958…⋅6.67843…4+3.92769…⋅6.67843…3−2.53776…⋅6.67843…2+2.05015…⋅6.67843…−0.92231…=9.32881E16u9=6.34414…
Δu9=∣6.34414…−6.67843…∣=0.33428…Δu9=0.33428…
u10=6.02653…:Δu10=0.31761…
f(u9)=6.34414…20−0.13232…⋅6.34414…19+0.94746…⋅6.34414…18−0.24843…⋅6.34414…17+0.91397…⋅6.34414…16−0.35197…⋅6.34414…15+0.89652…⋅6.34414…14−0.44594…⋅6.34414…13+0.89273…⋅6.34414…12−0.53284…⋅6.34414…11+0.90071…⋅6.34414…10−0.61470…⋅6.34414…9+0.91896…⋅6.34414…8−0.69325…⋅6.34414…7+0.94632…⋅6.34414…6−0.76991…⋅6.34414…5+0.98192…⋅6.34414…4−0.84592…⋅6.34414…3+1.02507…⋅6.34414…2−0.92231…⋅6.34414…+1.07532…=1.11801E16f′(u9)=20⋅6.34414…19−2.51418…⋅6.34414…18+17.05434…⋅6.34414…17−4.22331…⋅6.34414…16+14.62354…⋅6.34414…15−5.27956…⋅6.34414…14+12.55136…⋅6.34414…13−5.79734…⋅6.34414…12+10.71285…⋅6.34414…11−5.86129…⋅6.34414…10+9.00714…⋅6.34414…9−5.53237…⋅6.34414…8+7.35171…⋅6.34414…7−4.85277…⋅6.34414…6+5.67797…⋅6.34414…5−3.84958…⋅6.34414…4+3.92769…⋅6.34414…3−2.53776…⋅6.34414…2+2.05015…⋅6.34414…−0.92231…=3.52005E16u10=6.02653…
Δu10=∣6.02653…−6.34414…∣=0.31761…Δu10=0.31761…
u11=5.72476…:Δu11=0.30176…
f(u10)=6.02653…20−0.13232…⋅6.02653…19+0.94746…⋅6.02653…18−0.24843…⋅6.02653…17+0.91397…⋅6.02653…16−0.35197…⋅6.02653…15+0.89652…⋅6.02653…14−0.44594…⋅6.02653…13+0.89273…⋅6.02653…12−0.53284…⋅6.02653…11+0.90071…⋅6.02653…10−0.61470…⋅6.02653…9+0.91896…⋅6.02653…8−0.69325…⋅6.02653…7+0.94632…⋅6.02653…6−0.76991…⋅6.02653…5+0.98192…⋅6.02653…4−0.84592…⋅6.02653…3+1.02507…⋅6.02653…2−0.92231…⋅6.02653…+1.07532…=4.00816E15f′(u10)=20⋅6.02653…19−2.51418…⋅6.02653…18+17.05434…⋅6.02653…17−4.22331…⋅6.02653…16+14.62354…⋅6.02653…15−5.27956…⋅6.02653…14+12.55136…⋅6.02653…13−5.79734…⋅6.02653…12+10.71285…⋅6.02653…11−5.86129…⋅6.02653…10+9.00714…⋅6.02653…9−5.53237…⋅6.02653…8+7.35171…⋅6.02653…7−4.85277…⋅6.02653…6+5.67797…⋅6.02653…5−3.84958…⋅6.02653…4+3.92769…⋅6.02653…3−2.53776…⋅6.02653…2+2.05015…⋅6.02653…−0.92231…=1.32822E16u11=5.72476…
Δu11=∣5.72476…−6.02653…∣=0.30176…Δu11=0.30176…
u12=5.43804…:Δu12=0.28672…
f(u11)=5.72476…20−0.13232…⋅5.72476…19+0.94746…⋅5.72476…18−0.24843…⋅5.72476…17+0.91397…⋅5.72476…16−0.35197…⋅5.72476…15+0.89652…⋅5.72476…14−0.44594…⋅5.72476…13+0.89273…⋅5.72476…12−0.53284…⋅5.72476…11+0.90071…⋅5.72476…10−0.61470…⋅5.72476…9+0.91896…⋅5.72476…8−0.69325…⋅5.72476…7+0.94632…⋅5.72476…6−0.76991…⋅5.72476…5+0.98192…⋅5.72476…4−0.84592…⋅5.72476…3+1.02507…⋅5.72476…2−0.92231…⋅5.72476…+1.07532…=1.43697E15f′(u11)=20⋅5.72476…19−2.51418…⋅5.72476…18+17.05434…⋅5.72476…17−4.22331…⋅5.72476…16+14.62354…⋅5.72476…15−5.27956…⋅5.72476…14+12.55136…⋅5.72476…13−5.79734…⋅5.72476…12+10.71285…⋅5.72476…11−5.86129…⋅5.72476…10+9.00714…⋅5.72476…9−5.53237…⋅5.72476…8+7.35171…⋅5.72476…7−4.85277…⋅5.72476…6+5.67797…⋅5.72476…5−3.84958…⋅5.72476…4+3.92769…⋅5.72476…3−2.53776…⋅5.72476…2+2.05015…⋅5.72476…−0.92231…=5.01171E15u12=5.43804…
Δu12=∣5.43804…−5.72476…∣=0.28672…Δu12=0.28672…
u13=5.16561…:Δu13=0.27243…
f(u12)=5.43804…20−0.13232…⋅5.43804…19+0.94746…⋅5.43804…18−0.24843…⋅5.43804…17+0.91397…⋅5.43804…16−0.35197…⋅5.43804…15+0.89652…⋅5.43804…14−0.44594…⋅5.43804…13+0.89273…⋅5.43804…12−0.53284…⋅5.43804…11+0.90071…⋅5.43804…10−0.61470…⋅5.43804…9+0.91896…⋅5.43804…8−0.69325…⋅5.43804…7+0.94632…⋅5.43804…6−0.76991…⋅5.43804…5+0.98192…⋅5.43804…4−0.84592…⋅5.43804…3+1.02507…⋅5.43804…2−0.92231…⋅5.43804…+1.07532…=5.15177E14f′(u12)=20⋅5.43804…19−2.51418…⋅5.43804…18+17.05434…⋅5.43804…17−4.22331…⋅5.43804…16+14.62354…⋅5.43804…15−5.27956…⋅5.43804…14+12.55136…⋅5.43804…13−5.79734…⋅5.43804…12+10.71285…⋅5.43804…11−5.86129…⋅5.43804…10+9.00714…⋅5.43804…9−5.53237…⋅5.43804…8+7.35171…⋅5.43804…7−4.85277…⋅5.43804…6+5.67797…⋅5.43804…5−3.84958…⋅5.43804…4+3.92769…⋅5.43804…3−2.53776…⋅5.43804…2+2.05015…⋅5.43804…−0.92231…=1.89103E15u13=5.16561…
Δu13=∣5.16561…−5.43804…∣=0.27243…Δu13=0.27243…
u14=4.90675…:Δu14=0.25885…
f(u13)=5.16561…20−0.13232…⋅5.16561…19+0.94746…⋅5.16561…18−0.24843…⋅5.16561…17+0.91397…⋅5.16561…16−0.35197…⋅5.16561…15+0.89652…⋅5.16561…14−0.44594…⋅5.16561…13+0.89273…⋅5.16561…12−0.53284…⋅5.16561…11+0.90071…⋅5.16561…10−0.61470…⋅5.16561…9+0.91896…⋅5.16561…8−0.69325…⋅5.16561…7+0.94632…⋅5.16561…6−0.76991…⋅5.16561…5+0.98192…⋅5.16561…4−0.84592…⋅5.16561…3+1.02507…⋅5.16561…2−0.92231…⋅5.16561…+1.07532…=1.847E14f′(u13)=20⋅5.16561…19−2.51418…⋅5.16561…18+17.05434…⋅5.16561…17−4.22331…⋅5.16561…16+14.62354…⋅5.16561…15−5.27956…⋅5.16561…14+12.55136…⋅5.16561…13−5.79734…⋅5.16561…12+10.71285…⋅5.16561…11−5.86129…⋅5.16561…10+9.00714…⋅5.16561…9−5.53237…⋅5.16561…8+7.35171…⋅5.16561…7−4.85277…⋅5.16561…6+5.67797…⋅5.16561…5−3.84958…⋅5.16561…4+3.92769…⋅5.16561…3−2.53776…⋅5.16561…2+2.05015…⋅5.16561…−0.92231…=7.13524E14u14=4.90675…
Δu14=∣4.90675…−5.16561…∣=0.25885…Δu14=0.25885…
u15=4.66079…:Δu15=0.24596…
f(u14)=4.90675…20−0.13232…⋅4.90675…19+0.94746…⋅4.90675…18−0.24843…⋅4.90675…17+0.91397…⋅4.90675…16−0.35197…⋅4.90675…15+0.89652…⋅4.90675…14−0.44594…⋅4.90675…13+0.89273…⋅4.90675…12−0.53284…⋅4.90675…11+0.90071…⋅4.90675…10−0.61470…⋅4.90675…9+0.91896…⋅4.90675…8−0.69325…⋅4.90675…7+0.94632…⋅4.90675…6−0.76991…⋅4.90675…5+0.98192…⋅4.90675…4−0.84592…⋅4.90675…3+1.02507…⋅4.90675…2−0.92231…⋅4.90675…+1.07532…=6.62192E13f′(u14)=20⋅4.90675…19−2.51418…⋅4.90675…18+17.05434…⋅4.90675…17−4.22331…⋅4.90675…16+14.62354…⋅4.90675…15−5.27956…⋅4.90675…14+12.55136…⋅4.90675…13−5.79734…⋅4.90675…12+10.71285…⋅4.90675…11−5.86129…⋅4.90675…10+9.00714…⋅4.90675…9−5.53237…⋅4.90675…8+7.35171…⋅4.90675…7−4.85277…⋅4.90675…6+5.67797…⋅4.90675…5−3.84958…⋅4.90675…4+3.92769…⋅4.90675…3−2.53776…⋅4.90675…2+2.05015…⋅4.90675…−0.92231…=2.69224E14u15=4.66079…
Δu15=∣4.66079…−4.90675…∣=0.24596…Δu15=0.24596…
u16=4.42707…:Δu16=0.23371…
f(u15)=4.66079…20−0.13232…⋅4.66079…19+0.94746…⋅4.66079…18−0.24843…⋅4.66079…17+0.91397…⋅4.66079…16−0.35197…⋅4.66079…15+0.89652…⋅4.66079…14−0.44594…⋅4.66079…13+0.89273…⋅4.66079…12−0.53284…⋅4.66079…11+0.90071…⋅4.66079…10−0.61470…⋅4.66079…9+0.91896…⋅4.66079…8−0.69325…⋅4.66079…7+0.94632…⋅4.66079…6−0.76991…⋅4.66079…5+0.98192…⋅4.66079…4−0.84592…⋅4.66079…3+1.02507…⋅4.66079…2−0.92231…⋅4.66079…+1.07532…=2.37413E13f′(u15)=20⋅4.66079…19−2.51418…⋅4.66079…18+17.05434…⋅4.66079…17−4.22331…⋅4.66079…16+14.62354…⋅4.66079…15−5.27956…⋅4.66079…14+12.55136…⋅4.66079…13−5.79734…⋅4.66079…12+10.71285…⋅4.66079…11−5.86129…⋅4.66079…10+9.00714…⋅4.66079…9−5.53237…⋅4.66079…8+7.35171…⋅4.66079…7−4.85277…⋅4.66079…6+5.67797…⋅4.66079…5−3.84958…⋅4.66079…4+3.92769…⋅4.66079…3−2.53776…⋅4.66079…2+2.05015…⋅4.66079…−0.92231…=1.01581E14u16=4.42707…
Δu16=∣4.42707…−4.66079…∣=0.23371…Δu16=0.23371…
u17=4.20498…:Δu17=0.22208…
f(u16)=4.42707…20−0.13232…⋅4.42707…19+0.94746…⋅4.42707…18−0.24843…⋅4.42707…17+0.91397…⋅4.42707…16−0.35197…⋅4.42707…15+0.89652…⋅4.42707…14−0.44594…⋅4.42707…13+0.89273…⋅4.42707…12−0.53284…⋅4.42707…11+0.90071…⋅4.42707…10−0.61470…⋅4.42707…9+0.91896…⋅4.42707…8−0.69325…⋅4.42707…7+0.94632…⋅4.42707…6−0.76991…⋅4.42707…5+0.98192…⋅4.42707…4−0.84592…⋅4.42707…3+1.02507…⋅4.42707…2−0.92231…⋅4.42707…+1.07532…=8512005619076.098f′(u16)=20⋅4.42707…19−2.51418…⋅4.42707…18+17.05434…⋅4.42707…17−4.22331…⋅4.42707…16+14.62354…⋅4.42707…15−5.27956…⋅4.42707…14+12.55136…⋅4.42707…13−5.79734…⋅4.42707…12+10.71285…⋅4.42707…11−5.86129…⋅4.42707…10+9.00714…⋅4.42707…9−5.53237…⋅4.42707…8+7.35171…⋅4.42707…7−4.85277…⋅4.42707…6+5.67797…⋅4.42707…5−3.84958…⋅4.42707…4+3.92769…⋅4.42707…3−2.53776…⋅4.42707…2+2.05015…⋅4.42707…−0.92231…=3.83271E13u17=4.20498…
Δu17=∣4.20498…−4.42707…∣=0.22208…Δu17=0.22208…
u18=3.99394…:Δu18=0.21104…
f(u17)=4.20498…20−0.13232…⋅4.20498…19+0.94746…⋅4.20498…18−0.24843…⋅4.20498…17+0.91397…⋅4.20498…16−0.35197…⋅4.20498…15+0.89652…⋅4.20498…14−0.44594…⋅4.20498…13+0.89273…⋅4.20498…12−0.53284…⋅4.20498…11+0.90071…⋅4.20498…10−0.61470…⋅4.20498…9+0.91896…⋅4.20498…8−0.69325…⋅4.20498…7+0.94632…⋅4.20498…6−0.76991…⋅4.20498…5+0.98192…⋅4.20498…4−0.84592…⋅4.20498…3+1.02507…⋅4.20498…2−0.92231…⋅4.20498…+1.07532…=3051866396389.3633f′(u17)=20⋅4.20498…19−2.51418…⋅4.20498…18+17.05434…⋅4.20498…17−4.22331…⋅4.20498…16+14.62354…⋅4.20498…15−5.27956…⋅4.20498…14+12.55136…⋅4.20498…13−5.79734…⋅4.20498…12+10.71285…⋅4.20498…11−5.86129…⋅4.20498…10+9.00714…⋅4.20498…9−5.53237…⋅4.20498…8+7.35171…⋅4.20498…7−4.85277…⋅4.20498…6+5.67797…⋅4.20498…5−3.84958…⋅4.20498…4+3.92769…⋅4.20498…3−2.53776…⋅4.20498…2+2.05015…⋅4.20498…−0.92231…=1.44608E13u18=3.99394…
Δu18=∣3.99394…−4.20498…∣=0.21104…Δu18=0.21104…
u19=3.79338…:Δu19=0.20055…
f(u18)=3.99394…20−0.13232…⋅3.99394…19+0.94746…⋅3.99394…18−0.24843…⋅3.99394…17+0.91397…⋅3.99394…16−0.35197…⋅3.99394…15+0.89652…⋅3.99394…14−0.44594…⋅3.99394…13+0.89273…⋅3.99394…12−0.53284…⋅3.99394…11+0.90071…⋅3.99394…10−0.61470…⋅3.99394…9+0.91896…⋅3.99394…8−0.69325…⋅3.99394…7+0.94632…⋅3.99394…6−0.76991…⋅3.99394…5+0.98192…⋅3.99394…4−0.84592…⋅3.99394…3+1.02507…⋅3.99394…2−0.92231…⋅3.99394…+1.07532…=1094225069615.9116f′(u18)=20⋅3.99394…19−2.51418…⋅3.99394…18+17.05434…⋅3.99394…17−4.22331…⋅3.99394…16+14.62354…⋅3.99394…15−5.27956…⋅3.99394…14+12.55136…⋅3.99394…13−5.79734…⋅3.99394…12+10.71285…⋅3.99394…11−5.86129…⋅3.99394…10+9.00714…⋅3.99394…9−5.53237…⋅3.99394…8+7.35171…⋅3.99394…7−4.85277…⋅3.99394…6+5.67797…⋅3.99394…5−3.84958…⋅3.99394…4+3.92769…⋅3.99394…3−2.53776…⋅3.99394…2+2.05015…⋅3.99394…−0.92231…=5455965292045.312u19=3.79338…
Δu19=∣3.79338…−3.99394…∣=0.20055…Δu19=0.20055…
u20=3.60279…:Δu20=0.19059…
f(u19)=3.79338…20−0.13232…⋅3.79338…19+0.94746…⋅3.79338…18−0.24843…⋅3.79338…17+0.91397…⋅3.79338…16−0.35197…⋅3.79338…15+0.89652…⋅3.79338…14−0.44594…⋅3.79338…13+0.89273…⋅3.79338…12−0.53284…⋅3.79338…11+0.90071…⋅3.79338…10−0.61470…⋅3.79338…9+0.91896…⋅3.79338…8−0.69325…⋅3.79338…7+0.94632…⋅3.79338…6−0.76991…⋅3.79338…5+0.98192…⋅3.79338…4−0.84592…⋅3.79338…3+1.02507…⋅3.79338…2−0.92231…⋅3.79338…+1.07532…=392334398008.54114f′(u19)=20⋅3.79338…19−2.51418…⋅3.79338…18+17.05434…⋅3.79338…17−4.22331…⋅3.79338…16+14.62354…⋅3.79338…15−5.27956…⋅3.79338…14+12.55136…⋅3.79338…13−5.79734…⋅3.79338…12+10.71285…⋅3.79338…11−5.86129…⋅3.79338…10+9.00714…⋅3.79338…9−5.53237…⋅3.79338…8+7.35171…⋅3.79338…7−4.85277…⋅3.79338…6+5.67797…⋅3.79338…5−3.84958…⋅3.79338…4+3.92769…⋅3.79338…3−2.53776…⋅3.79338…2+2.05015…⋅3.79338…−0.92231…=2058458229104.9626u20=3.60279…
Δu20=∣3.60279…−3.79338…∣=0.19059…Δu20=0.19059…
u21=3.42165…:Δu21=0.18113…
f(u20)=3.60279…20−0.13232…⋅3.60279…19+0.94746…⋅3.60279…18−0.24843…⋅3.60279…17+0.91397…⋅3.60279…16−0.35197…⋅3.60279…15+0.89652…⋅3.60279…14−0.44594…⋅3.60279…13+0.89273…⋅3.60279…12−0.53284…⋅3.60279…11+0.90071…⋅3.60279…10−0.61470…⋅3.60279…9+0.91896…⋅3.60279…8−0.69325…⋅3.60279…7+0.94632…⋅3.60279…6−0.76991…⋅3.60279…5+0.98192…⋅3.60279…4−0.84592…⋅3.60279…3+1.02507…⋅3.60279…2−0.92231…⋅3.60279…+1.07532…=140674678734.53632f′(u20)=20⋅3.60279…19−2.51418…⋅3.60279…18+17.05434…⋅3.60279…17−4.22331…⋅3.60279…16+14.62354…⋅3.60279…15−5.27956…⋅3.60279…14+12.55136…⋅3.60279…13−5.79734…⋅3.60279…12+10.71285…⋅3.60279…11−5.86129…⋅3.60279…10+9.00714…⋅3.60279…9−5.53237…⋅3.60279…8+7.35171…⋅3.60279…7−4.85277…⋅3.60279…6+5.67797…⋅3.60279…5−3.84958…⋅3.60279…4+3.92769…⋅3.60279…3−2.53776…⋅3.60279…2+2.05015…⋅3.60279…−0.92231…=776609292794.6857u21=3.42165…
Δu21=∣3.42165…−3.60279…∣=0.18113…Δu21=0.18113…
u22=3.24949…:Δu22=0.17216…
f(u21)=3.42165…20−0.13232…⋅3.42165…19+0.94746…⋅3.42165…18−0.24843…⋅3.42165…17+0.91397…⋅3.42165…16−0.35197…⋅3.42165…15+0.89652…⋅3.42165…14−0.44594…⋅3.42165…13+0.89273…⋅3.42165…12−0.53284…⋅3.42165…11+0.90071…⋅3.42165…10−0.61470…⋅3.42165…9+0.91896…⋅3.42165…8−0.69325…⋅3.42165…7+0.94632…⋅3.42165…6−0.76991…⋅3.42165…5+0.98192…⋅3.42165…4−0.84592…⋅3.42165…3+1.02507…⋅3.42165…2−0.92231…⋅3.42165…+1.07532…=50441356117.7277f′(u21)=20⋅3.42165…19−2.51418…⋅3.42165…18+17.05434…⋅3.42165…17−4.22331…⋅3.42165…16+14.62354…⋅3.42165…15−5.27956…⋅3.42165…14+12.55136…⋅3.42165…13−5.79734…⋅3.42165…12+10.71285…⋅3.42165…11−5.86129…⋅3.42165…10+9.00714…⋅3.42165…9−5.53237…⋅3.42165…8+7.35171…⋅3.42165…7−4.85277…⋅3.42165…6+5.67797…⋅3.42165…5−3.84958…⋅3.42165…4+3.92769…⋅3.42165…3−2.53776…⋅3.42165…2+2.05015…⋅3.42165…−0.92231…=292989246903.27985u22=3.24949…
Δu22=∣3.24949…−3.42165…∣=0.17216…Δu22=0.17216…
u23=3.08585…:Δu23=0.16363…
f(u22)=3.24949…20−0.13232…⋅3.24949…19+0.94746…⋅3.24949…18−0.24843…⋅3.24949…17+0.91397…⋅3.24949…16−0.35197…⋅3.24949…15+0.89652…⋅3.24949…14−0.44594…⋅3.24949…13+0.89273…⋅3.24949…12−0.53284…⋅3.24949…11+0.90071…⋅3.24949…10−0.61470…⋅3.24949…9+0.91896…⋅3.24949…8−0.69325…⋅3.24949…7+0.94632…⋅3.24949…6−0.76991…⋅3.24949…5+0.98192…⋅3.24949…4−0.84592…⋅3.24949…3+1.02507…⋅3.24949…2−0.92231…⋅3.24949…+1.07532…=18087168372.42657f′(u22)=20⋅3.24949…19−2.51418…⋅3.24949…18+17.05434…⋅3.24949…17−4.22331…⋅3.24949…16+14.62354…⋅3.24949…15−5.27956…⋅3.24949…14+12.55136…⋅3.24949…13−5.79734…⋅3.24949…12+10.71285…⋅3.24949…11−5.86129…⋅3.24949…10+9.00714…⋅3.24949…9−5.53237…⋅3.24949…8+7.35171…⋅3.24949…7−4.85277…⋅3.24949…6+5.67797…⋅3.24949…5−3.84958…⋅3.24949…4+3.92769…⋅3.24949…3−2.53776…⋅3.24949…2+2.05015…⋅3.24949…−0.92231…=110531886486.75546u23=3.08585…
Δu23=∣3.08585…−3.24949…∣=0.16363…Δu23=0.16363…
u24=2.93030…:Δu24=0.15554…
f(u23)=3.08585…20−0.13232…⋅3.08585…19+0.94746…⋅3.08585…18−0.24843…⋅3.08585…17+0.91397…⋅3.08585…16−0.35197…⋅3.08585…15+0.89652…⋅3.08585…14−0.44594…⋅3.08585…13+0.89273…⋅3.08585…12−0.53284…⋅3.08585…11+0.90071…⋅3.08585…10−0.61470…⋅3.08585…9+0.91896…⋅3.08585…8−0.69325…⋅3.08585…7+0.94632…⋅3.08585…6−0.76991…⋅3.08585…5+0.98192…⋅3.08585…4−0.84592…⋅3.08585…3+1.02507…⋅3.08585…2−0.92231…⋅3.08585…+1.07532…=6485888494.52872…f′(u23)=20⋅3.08585…19−2.51418…⋅3.08585…18+17.05434…⋅3.08585…17−4.22331…⋅3.08585…16+14.62354…⋅3.08585…15−5.27956…⋅3.08585…14+12.55136…⋅3.08585…13−5.79734…⋅3.08585…12+10.71285…⋅3.08585…11−5.86129…⋅3.08585…10+9.00714…⋅3.08585…9−5.53237…⋅3.08585…8+7.35171…⋅3.08585…7−4.85277…⋅3.08585…6+5.67797…⋅3.08585…5−3.84958…⋅3.08585…4+3.92769…⋅3.08585…3−2.53776…⋅3.08585…2+2.05015…⋅3.08585…−0.92231…=41697322133.39375u24=2.93030…
Δu24=∣2.93030…−3.08585…∣=0.15554…Δu24=0.15554…
u25=2.78243…:Δu25=0.14786…
f(u24)=2.93030…20−0.13232…⋅2.93030…19+0.94746…⋅2.93030…18−0.24843…⋅2.93030…17+0.91397…⋅2.93030…16−0.35197…⋅2.93030…15+0.89652…⋅2.93030…14−0.44594…⋅2.93030…13+0.89273…⋅2.93030…12−0.53284…⋅2.93030…11+0.90071…⋅2.93030…10−0.61470…⋅2.93030…9+0.91896…⋅2.93030…8−0.69325…⋅2.93030…7+0.94632…⋅2.93030…6−0.76991…⋅2.93030…5+0.98192…⋅2.93030…4−0.84592…⋅2.93030…3+1.02507…⋅2.93030…2−0.92231…⋅2.93030…+1.07532…=2325872621.57641…f′(u24)=20⋅2.93030…19−2.51418…⋅2.93030…18+17.05434…⋅2.93030…17−4.22331…⋅2.93030…16+14.62354…⋅2.93030…15−5.27956…⋅2.93030…14+12.55136…⋅2.93030…13−5.79734…⋅2.93030…12+10.71285…⋅2.93030…11−5.86129…⋅2.93030…10+9.00714…⋅2.93030…9−5.53237…⋅2.93030…8+7.35171…⋅2.93030…7−4.85277…⋅2.93030…6+5.67797…⋅2.93030…5−3.84958…⋅2.93030…4+3.92769…⋅2.93030…3−2.53776…⋅2.93030…2+2.05015…⋅2.93030…−0.92231…=15729353429.86823u25=2.78243…
Δu25=∣2.78243…−2.93030…∣=0.14786…Δu25=0.14786…
u26=2.64185…:Δu26=0.14058…
f(u25)=2.78243…20−0.13232…⋅2.78243…19+0.94746…⋅2.78243…18−0.24843…⋅2.78243…17+0.91397…⋅2.78243…16−0.35197…⋅2.78243…15+0.89652…⋅2.78243…14−0.44594…⋅2.78243…13+0.89273…⋅2.78243…12−0.53284…⋅2.78243…11+0.90071…⋅2.78243…10−0.61470…⋅2.78243…9+0.91896…⋅2.78243…8−0.69325…⋅2.78243…7+0.94632…⋅2.78243…6−0.76991…⋅2.78243…5+0.98192…⋅2.78243…4−0.84592…⋅2.78243…3+1.02507…⋅2.78243…2−0.92231…⋅2.78243…+1.07532…=834109250.35724…f′(u25)=20⋅2.78243…19−2.51418…⋅2.78243…18+17.05434…⋅2.78243…17−4.22331…⋅2.78243…16+14.62354…⋅2.78243…15−5.27956…⋅2.78243…14+12.55136…⋅2.78243…13−5.79734…⋅2.78243…12+10.71285…⋅2.78243…11−5.86129…⋅2.78243…10+9.00714…⋅2.78243…9−5.53237…⋅2.78243…8+7.35171…⋅2.78243…7−4.85277…⋅2.78243…6+5.67797…⋅2.78243…5−3.84958…⋅2.78243…4+3.92769…⋅2.78243…3−2.53776…⋅2.78243…2+2.05015…⋅2.78243…−0.92231…=5933249204.22549…u26=2.64185…
Δu26=∣2.64185…−2.78243…∣=0.14058…Δu26=0.14058…
u27=2.50818…:Δu27=0.13367…
f(u26)=2.64185…20−0.13232…⋅2.64185…19+0.94746…⋅2.64185…18−0.24843…⋅2.64185…17+0.91397…⋅2.64185…16−0.35197…⋅2.64185…15+0.89652…⋅2.64185…14−0.44594…⋅2.64185…13+0.89273…⋅2.64185…12−0.53284…⋅2.64185…11+0.90071…⋅2.64185…10−0.61470…⋅2.64185…9+0.91896…⋅2.64185…8−0.69325…⋅2.64185…7+0.94632…⋅2.64185…6−0.76991…⋅2.64185…5+0.98192…⋅2.64185…4−0.84592…⋅2.64185…3+1.02507…⋅2.64185…2−0.92231…⋅2.64185…+1.07532…=299146684.78340…f′(u26)=20⋅2.64185…19−2.51418…⋅2.64185…18+17.05434…⋅2.64185…17−4.22331…⋅2.64185…16+14.62354…⋅2.64185…15−5.27956…⋅2.64185…14+12.55136…⋅2.64185…13−5.79734…⋅2.64185…12+10.71285…⋅2.64185…11−5.86129…⋅2.64185…10+9.00714…⋅2.64185…9−5.53237…⋅2.64185…8+7.35171…⋅2.64185…7−4.85277…⋅2.64185…6+5.67797…⋅2.64185…5−3.84958…⋅2.64185…4+3.92769…⋅2.64185…3−2.53776…⋅2.64185…2+2.05015…⋅2.64185…−0.92231…=2237945483.37649…u27=2.50818…
Δu27=∣2.50818…−2.64185…∣=0.13367…Δu27=0.13367…
u28=2.38106…:Δu28=0.12711…
f(u27)=2.50818…20−0.13232…⋅2.50818…19+0.94746…⋅2.50818…18−0.24843…⋅2.50818…17+0.91397…⋅2.50818…16−0.35197…⋅2.50818…15+0.89652…⋅2.50818…14−0.44594…⋅2.50818…13+0.89273…⋅2.50818…12−0.53284…⋅2.50818…11+0.90071…⋅2.50818…10−0.61470…⋅2.50818…9+0.91896…⋅2.50818…8−0.69325…⋅2.50818…7+0.94632…⋅2.50818…6−0.76991…⋅2.50818…5+0.98192…⋅2.50818…4−0.84592…⋅2.50818…3+1.02507…⋅2.50818…2−0.92231…⋅2.50818…+1.07532…=107293705.94086…f′(u27)=20⋅2.50818…19−2.51418…⋅2.50818…18+17.05434…⋅2.50818…17−4.22331…⋅2.50818…16+14.62354…⋅2.50818…15−5.27956…⋅2.50818…14+12.55136…⋅2.50818…13−5.79734…⋅2.50818…12+10.71285…⋅2.50818…11−5.86129…⋅2.50818…10+9.00714…⋅2.50818…9−5.53237…⋅2.50818…8+7.35171…⋅2.50818…7−4.85277…⋅2.50818…6+5.67797…⋅2.50818…5−3.84958…⋅2.50818…4+3.92769…⋅2.50818…3−2.53776…⋅2.50818…2+2.05015…⋅2.50818…−0.92231…=844066913.94210…u28=2.38106…
Δu28=∣2.38106…−2.50818…∣=0.12711…Δu28=0.12711…
u29=2.26016…:Δu29=0.12090…
f(u28)=2.38106…20−0.13232…⋅2.38106…19+0.94746…⋅2.38106…18−0.24843…⋅2.38106…17+0.91397…⋅2.38106…16−0.35197…⋅2.38106…15+0.89652…⋅2.38106…14−0.44594…⋅2.38106…13+0.89273…⋅2.38106…12−0.53284…⋅2.38106…11+0.90071…⋅2.38106…10−0.61470…⋅2.38106…9+0.91896…⋅2.38106…8−0.69325…⋅2.38106…7+0.94632…⋅2.38106…6−0.76991…⋅2.38106…5+0.98192…⋅2.38106…4−0.84592…⋅2.38106…3+1.02507…⋅2.38106…2−0.92231…⋅2.38106…+1.07532…=38485645.39091…f′(u28)=20⋅2.38106…19−2.51418…⋅2.38106…18+17.05434…⋅2.38106…17−4.22331…⋅2.38106…16+14.62354…⋅2.38106…15−5.27956…⋅2.38106…14+12.55136…⋅2.38106…13−5.79734…⋅2.38106…12+10.71285…⋅2.38106…11−5.86129…⋅2.38106…10+9.00714…⋅2.38106…9−5.53237…⋅2.38106…8+7.35171…⋅2.38106…7−4.85277…⋅2.38106…6+5.67797…⋅2.38106…5−3.84958…⋅2.38106…4+3.92769…⋅2.38106…3−2.53776…⋅2.38106…2+2.05015…⋅2.38106…−0.92231…=318323556.38546…u29=2.26016…
Δu29=∣2.26016…−2.38106…∣=0.12090…Δu29=0.12090…
u30=2.14515…:Δu30=0.11501…
f(u29)=2.26016…20−0.13232…⋅2.26016…19+0.94746…⋅2.26016…18−0.24843…⋅2.26016…17+0.91397…⋅2.26016…16−0.35197…⋅2.26016…15+0.89652…⋅2.26016…14−0.44594…⋅2.26016…13+0.89273…⋅2.26016…12−0.53284…⋅2.26016…11+0.90071…⋅2.26016…10−0.61470…⋅2.26016…9+0.91896…⋅2.26016…8−0.69325…⋅2.26016…7+0.94632…⋅2.26016…6−0.76991…⋅2.26016…5+0.98192…⋅2.26016…4−0.84592…⋅2.26016…3+1.02507…⋅2.26016…2−0.92231…⋅2.26016…+1.07532…=13805907.36855…f′(u29)=20⋅2.26016…19−2.51418…⋅2.26016…18+17.05434…⋅2.26016…17−4.22331…⋅2.26016…16+14.62354…⋅2.26016…15−5.27956…⋅2.26016…14+12.55136…⋅2.26016…13−5.79734…⋅2.26016…12+10.71285…⋅2.26016…11−5.86129…⋅2.26016…10+9.00714…⋅2.26016…9−5.53237…⋅2.26016…8+7.35171…⋅2.26016…7−4.85277…⋅2.26016…6+5.67797…⋅2.26016…5−3.84958…⋅2.26016…4+3.92769…⋅2.26016…3−2.53776…⋅2.26016…2+2.05015…⋅2.26016…−0.92231…=120037702.84139…u30=2.14515…
Δu30=∣2.14515…−2.26016…∣=0.11501…Δu30=0.11501…
u31=2.03571…:Δu31=0.10943…
f(u30)=2.14515…20−0.13232…⋅2.14515…19+0.94746…⋅2.14515…18−0.24843…⋅2.14515…17+0.91397…⋅2.14515…16−0.35197…⋅2.14515…15+0.89652…⋅2.14515…14−0.44594…⋅2.14515…13+0.89273…⋅2.14515…12−0.53284…⋅2.14515…11+0.90071…⋅2.14515…10−0.61470…⋅2.14515…9+0.91896…⋅2.14515…8−0.69325…⋅2.14515…7+0.94632…⋅2.14515…6−0.76991…⋅2.14515…5+0.98192…⋅2.14515…4−0.84592…⋅2.14515…3+1.02507…⋅2.14515…2−0.92231…⋅2.14515…+1.07532…=4953155.70135…f′(u30)=20⋅2.14515…19−2.51418…⋅2.14515…18+17.05434…⋅2.14515…17−4.22331…⋅2.14515…16+14.62354…⋅2.14515…15−5.27956…⋅2.14515…14+12.55136…⋅2.14515…13−5.79734…⋅2.14515…12+10.71285…⋅2.14515…11−5.86129…⋅2.14515…10+9.00714…⋅2.14515…9−5.53237…⋅2.14515…8+7.35171…⋅2.14515…7−4.85277…⋅2.14515…6+5.67797…⋅2.14515…5−3.84958…⋅2.14515…4+3.92769…⋅2.14515…3−2.53776…⋅2.14515…2+2.05015…⋅2.14515…−0.92231…=45259930.04439…u31=2.03571…
Δu31=∣2.03571…−2.14515…∣=0.10943…Δu31=0.10943…
u32=1.93155…:Δu32=0.10416…
f(u31)=2.03571…20−0.13232…⋅2.03571…19+0.94746…⋅2.03571…18−0.24843…⋅2.03571…17+0.91397…⋅2.03571…16−0.35197…⋅2.03571…15+0.89652…⋅2.03571…14−0.44594…⋅2.03571…13+0.89273…⋅2.03571…12−0.53284…⋅2.03571…11+0.90071…⋅2.03571…10−0.61470…⋅2.03571…9+0.91896…⋅2.03571…8−0.69325…⋅2.03571…7+0.94632…⋅2.03571…6−0.76991…⋅2.03571…5+0.98192…⋅2.03571…4−0.84592…⋅2.03571…3+1.02507…⋅2.03571…2−0.92231…⋅2.03571…+1.07532…=1777304.31243…f′(u31)=20⋅2.03571…19−2.51418…⋅2.03571…18+17.05434…⋅2.03571…17−4.22331…⋅2.03571…16+14.62354…⋅2.03571…15−5.27956…⋅2.03571…14+12.55136…⋅2.03571…13−5.79734…⋅2.03571…12+10.71285…⋅2.03571…11−5.86129…⋅2.03571…10+9.00714…⋅2.03571…9−5.53237…⋅2.03571…8+7.35171…⋅2.03571…7−4.85277…⋅2.03571…6+5.67797…⋅2.03571…5−3.84958…⋅2.03571…4+3.92769…⋅2.03571…3−2.53776…⋅2.03571…2+2.05015…⋅2.03571…−0.92231…=17062580.63349…u32=1.93155…
Δu32=∣1.93155…−2.03571…∣=0.10416…Δu32=0.10416…
u33=1.83237…:Δu33=0.09918…
f(u32)=1.93155…20−0.13232…⋅1.93155…19+0.94746…⋅1.93155…18−0.24843…⋅1.93155…17+0.91397…⋅1.93155…16−0.35197…⋅1.93155…15+0.89652…⋅1.93155…14−0.44594…⋅1.93155…13+0.89273…⋅1.93155…12−0.53284…⋅1.93155…11+0.90071…⋅1.93155…10−0.61470…⋅1.93155…9+0.91896…⋅1.93155…8−0.69325…⋅1.93155…7+0.94632…⋅1.93155…6−0.76991…⋅1.93155…5+0.98192…⋅1.93155…4−0.84592…⋅1.93155…3+1.02507…⋅1.93155…2−0.92231…⋅1.93155…+1.07532…=637852.40185…f′(u32)=20⋅1.93155…19−2.51418…⋅1.93155…18+17.05434…⋅1.93155…17−4.22331…⋅1.93155…16+14.62354…⋅1.93155…15−5.27956…⋅1.93155…14+12.55136…⋅1.93155…13−5.79734…⋅1.93155…12+10.71285…⋅1.93155…11−5.86129…⋅1.93155…10+9.00714…⋅1.93155…9−5.53237…⋅1.93155…8+7.35171…⋅1.93155…7−4.85277…⋅1.93155…6+5.67797…⋅1.93155…5−3.84958…⋅1.93155…4+3.92769…⋅1.93155…3−2.53776…⋅1.93155…2+2.05015…⋅1.93155…−0.92231…=6431219.39917…u33=1.83237…
Δu33=∣1.83237…−1.93155…∣=0.09918…Δu33=0.09918…
u34=1.73789…:Δu34=0.09448…
f(u33)=1.83237…20−0.13232…⋅1.83237…19+0.94746…⋅1.83237…18−0.24843…⋅1.83237…17+0.91397…⋅1.83237…16−0.35197…⋅1.83237…15+0.89652…⋅1.83237…14−0.44594…⋅1.83237…13+0.89273…⋅1.83237…12−0.53284…⋅1.83237…11+0.90071…⋅1.83237…10−0.61470…⋅1.83237…9+0.91896…⋅1.83237…8−0.69325…⋅1.83237…7+0.94632…⋅1.83237…6−0.76991…⋅1.83237…5+0.98192…⋅1.83237…4−0.84592…⋅1.83237…3+1.02507…⋅1.83237…2−0.92231…⋅1.83237…+1.07532…=228969.95201…f′(u33)=20⋅1.83237…19−2.51418…⋅1.83237…18+17.05434…⋅1.83237…17−4.22331…⋅1.83237…16+14.62354…⋅1.83237…15−5.27956…⋅1.83237…14+12.55136…⋅1.83237…13−5.79734…⋅1.83237…12+10.71285…⋅1.83237…11−5.86129…⋅1.83237…10+9.00714…⋅1.83237…9−5.53237…⋅1.83237…8+7.35171…⋅1.83237…7−4.85277…⋅1.83237…6+5.67797…⋅1.83237…5−3.84958…⋅1.83237…4+3.92769…⋅1.83237…3−2.53776…⋅1.83237…2+2.05015…⋅1.83237…−0.92231…=2423465.11137…u34=1.73789…
Δu34=∣1.73789…−1.83237…∣=0.09448…Δu34=0.09448…
u35=1.64783…:Δu35=0.09005…
f(u34)=1.73789…20−0.13232…⋅1.73789…19+0.94746…⋅1.73789…18−0.24843…⋅1.73789…17+0.91397…⋅1.73789…16−0.35197…⋅1.73789…15+0.89652…⋅1.73789…14−0.44594…⋅1.73789…13+0.89273…⋅1.73789…12−0.53284…⋅1.73789…11+0.90071…⋅1.73789…10−0.61470…⋅1.73789…9+0.91896…⋅1.73789…8−0.69325…⋅1.73789…7+0.94632…⋅1.73789…6−0.76991…⋅1.73789…5+0.98192…⋅1.73789…4−0.84592…⋅1.73789…3+1.02507…⋅1.73789…2−0.92231…⋅1.73789…+1.07532…=82217.85317…f′(u34)=20⋅1.73789…19−2.51418…⋅1.73789…18+17.05434…⋅1.73789…17−4.22331…⋅1.73789…16+14.62354…⋅1.73789…15−5.27956…⋅1.73789…14+12.55136…⋅1.73789…13−5.79734…⋅1.73789…12+10.71285…⋅1.73789…11−5.86129…⋅1.73789…10+9.00714…⋅1.73789…9−5.53237…⋅1.73789…8+7.35171…⋅1.73789…7−4.85277…⋅1.73789…6+5.67797…⋅1.73789…5−3.84958…⋅1.73789…4+3.92769…⋅1.73789…3−2.53776…⋅1.73789…2+2.05015…⋅1.73789…−0.92231…=912941.74704…u35=1.64783…
Δu35=∣1.64783…−1.73789…∣=0.09005…Δu35=0.09005…
u36=1.56192…:Δu36=0.08591…
f(u35)=1.64783…20−0.13232…⋅1.64783…19+0.94746…⋅1.64783…18−0.24843…⋅1.64783…17+0.91397…⋅1.64783…16−0.35197…⋅1.64783…15+0.89652…⋅1.64783…14−0.44594…⋅1.64783…13+0.89273…⋅1.64783…12−0.53284…⋅1.64783…11+0.90071…⋅1.64783…10−0.61470…⋅1.64783…9+0.91896…⋅1.64783…8−0.69325…⋅1.64783…7+0.94632…⋅1.64783…6−0.76991…⋅1.64783…5+0.98192…⋅1.64783…4−0.84592…⋅1.64783…3+1.02507…⋅1.64783…2−0.92231…⋅1.64783…+1.07532…=29534.18496…f′(u35)=20⋅1.64783…19−2.51418…⋅1.64783…18+17.05434…⋅1.64783…17−4.22331…⋅1.64783…16+14.62354…⋅1.64783…15−5.27956…⋅1.64783…14+12.55136…⋅1.64783…13−5.79734…⋅1.64783…12+10.71285…⋅1.64783…11−5.86129…⋅1.64783…10+9.00714…⋅1.64783…9−5.53237…⋅1.64783…8+7.35171…⋅1.64783…7−4.85277…⋅1.64783…6+5.67797…⋅1.64783…5−3.84958…⋅1.64783…4+3.92769…⋅1.64783…3−2.53776…⋅1.64783…2+2.05015…⋅1.64783…−0.92231…=343768.57567…u36=1.56192…
Δu36=∣1.56192…−1.64783…∣=0.08591…Δu36=0.08591…
u37=1.47987…:Δu37=0.08205…
f(u36)=1.56192…20−0.13232…⋅1.56192…19+0.94746…⋅1.56192…18−0.24843…⋅1.56192…17+0.91397…⋅1.56192…16−0.35197…⋅1.56192…15+0.89652…⋅1.56192…14−0.44594…⋅1.56192…13+0.89273…⋅1.56192…12−0.53284…⋅1.56192…11+0.90071…⋅1.56192…10−0.61470…⋅1.56192…9+0.91896…⋅1.56192…8−0.69325…⋅1.56192…7+0.94632…⋅1.56192…6−0.76991…⋅1.56192…5+0.98192…⋅1.56192…4−0.84592…⋅1.56192…3+1.02507…⋅1.56192…2−0.92231…⋅1.56192…+1.07532…=10614.92209…f′(u36)=20⋅1.56192…19−2.51418…⋅1.56192…18+17.05434…⋅1.56192…17−4.22331…⋅1.56192…16+14.62354…⋅1.56192…15−5.27956…⋅1.56192…14+12.55136…⋅1.56192…13−5.79734…⋅1.56192…12+10.71285…⋅1.56192…11−5.86129…⋅1.56192…10+9.00714…⋅1.56192…9−5.53237…⋅1.56192…8+7.35171…⋅1.56192…7−4.85277…⋅1.56192…6+5.67797…⋅1.56192…5−3.84958…⋅1.56192…4+3.92769…⋅1.56192…3−2.53776…⋅1.56192…2+2.05015…⋅1.56192…−0.92231…=129371.07934…u37=1.47987…
Δu37=∣1.47987…−1.56192…∣=0.08205…Δu37=0.08205…
u38=1.40138…:Δu38=0.07848…
f(u37)=1.47987…20−0.13232…⋅1.47987…19+0.94746…⋅1.47987…18−0.24843…⋅1.47987…17+0.91397…⋅1.47987…16−0.35197…⋅1.47987…15+0.89652…⋅1.47987…14−0.44594…⋅1.47987…13+0.89273…⋅1.47987…12−0.53284…⋅1.47987…11+0.90071…⋅1.47987…10−0.61470…⋅1.47987…9+0.91896…⋅1.47987…8−0.69325…⋅1.47987…7+0.94632…⋅1.47987…6−0.76991…⋅1.47987…5+0.98192…⋅1.47987…4−0.84592…⋅1.47987…3+1.02507…⋅1.47987…2−0.92231…⋅1.47987…+1.07532…=3818.00816…f′(u37)=20⋅1.47987…19−2.51418…⋅1.47987…18+17.05434…⋅1.47987…17−4.22331…⋅1.47987…16+14.62354…⋅1.47987…15−5.27956…⋅1.47987…14+12.55136…⋅1.47987…13−5.79734…⋅1.47987…12+10.71285…⋅1.47987…11−5.86129…⋅1.47987…10+9.00714…⋅1.47987…9−5.53237…⋅1.47987…8+7.35171…⋅1.47987…7−4.85277…⋅1.47987…6+5.67797…⋅1.47987…5−3.84958…⋅1.47987…4+3.92769…⋅1.47987…3−2.53776…⋅1.47987…2+2.05015…⋅1.47987…−0.92231…=48646.07932…u38=1.40138…
Δu38=∣1.40138…−1.47987…∣=0.07848…Δu38=0.07848…
u39=1.32613…:Δu39=0.07525…
f(u38)=1.40138…20−0.13232…⋅1.40138…19+0.94746…⋅1.40138…18−0.24843…⋅1.40138…17+0.91397…⋅1.40138…16−0.35197…⋅1.40138…15+0.89652…⋅1.40138…14−0.44594…⋅1.40138…13+0.89273…⋅1.40138…12−0.53284…⋅1.40138…11+0.90071…⋅1.40138…10−0.61470…⋅1.40138…9+0.91896…⋅1.40138…8−0.69325…⋅1.40138…7+0.94632…⋅1.40138…6−0.76991…⋅1.40138…5+0.98192…⋅1.40138…4−0.84592…⋅1.40138…3+1.02507…⋅1.40138…2−0.92231…⋅1.40138…+1.07532…=1374.80347…f′(u38)=20⋅1.40138…19−2.51418…⋅1.40138…18+17.05434…⋅1.40138…17−4.22331…⋅1.40138…16+14.62354…⋅1.40138…15−5.27956…⋅1.40138…14+12.55136…⋅1.40138…13−5.79734…⋅1.40138…12+10.71285…⋅1.40138…11−5.86129…⋅1.40138…10+9.00714…⋅1.40138…9−5.53237…⋅1.40138…8+7.35171…⋅1.40138…7−4.85277…⋅1.40138…6+5.67797…⋅1.40138…5−3.84958…⋅1.40138…4+3.92769…⋅1.40138…3−2.53776…⋅1.40138…2+2.05015…⋅1.40138…−0.92231…=18269.09923…u39=1.32613…
Δu39=∣1.32613…−1.40138…∣=0.07525…Δu39=0.07525…
u40=1.25370…:Δu40=0.07242…
f(u39)=1.32613…20−0.13232…⋅1.32613…19+0.94746…⋅1.32613…18−0.24843…⋅1.32613…17+0.91397…⋅1.32613…16−0.35197…⋅1.32613…15+0.89652…⋅1.32613…14−0.44594…⋅1.32613…13+0.89273…⋅1.32613…12−0.53284…⋅1.32613…11+0.90071…⋅1.32613…10−0.61470…⋅1.32613…9+0.91896…⋅1.32613…8−0.69325…⋅1.32613…7+0.94632…⋅1.32613…6−0.76991…⋅1.32613…5+0.98192…⋅1.32613…4−0.84592…⋅1.32613…3+1.02507…⋅1.32613…2−0.92231…⋅1.32613…+1.07532…=495.90652…f′(u39)=20⋅1.32613…19−2.51418…⋅1.32613…18+17.05434…⋅1.32613…17−4.22331…⋅1.32613…16+14.62354…⋅1.32613…15−5.27956…⋅1.32613…14+12.55136…⋅1.32613…13−5.79734…⋅1.32613…12+10.71285…⋅1.32613…11−5.86129…⋅1.32613…10+9.00714…⋅1.32613…9−5.53237…⋅1.32613…8+7.35171…⋅1.32613…7−4.85277…⋅1.32613…6+5.67797…⋅1.32613…5−3.84958…⋅1.32613…4+3.92769…⋅1.32613…3−2.53776…⋅1.32613…2+2.05015…⋅1.32613…−0.92231…=6847.31085…u40=1.25370…
Δu40=∣1.25370…−1.32613…∣=0.07242…Δu40=0.07242…
u41=1.18356…:Δu41=0.07014…
f(u40)=1.25370…20−0.13232…⋅1.25370…19+0.94746…⋅1.25370…18−0.24843…⋅1.25370…17+0.91397…⋅1.25370…16−0.35197…⋅1.25370…15+0.89652…⋅1.25370…14−0.44594…⋅1.25370…13+0.89273…⋅1.25370…12−0.53284…⋅1.25370…11+0.90071…⋅1.25370…10−0.61470…⋅1.25370…9+0.91896…⋅1.25370…8−0.69325…⋅1.25370…7+0.94632…⋅1.25370…6−0.76991…⋅1.25370…5+0.98192…⋅1.25370…4−0.84592…⋅1.25370…3+1.02507…⋅1.25370…2−0.92231…⋅1.25370…+1.07532…=179.40175…f′(u40)=20⋅1.25370…19−2.51418…⋅1.25370…18+17.05434…⋅1.25370…17−4.22331…⋅1.25370…16+14.62354…⋅1.25370…15−5.27956…⋅1.25370…14+12.55136…⋅1.25370…13−5.79734…⋅1.25370…12+10.71285…⋅1.25370…11−5.86129…⋅1.25370…10+9.00714…⋅1.25370…9−5.53237…⋅1.25370…8+7.35171…⋅1.25370…7−4.85277…⋅1.25370…6+5.67797…⋅1.25370…5−3.84958…⋅1.25370…4+3.92769…⋅1.25370…3−2.53776…⋅1.25370…2+2.05015…⋅1.25370…−0.92231…=2557.55243…u41=1.18356…
Δu41=∣1.18356…−1.25370…∣=0.07014…Δu41=0.07014…
u42=1.11481…:Δu42=0.06874…
f(u41)=1.18356…20−0.13232…⋅1.18356…19+0.94746…⋅1.18356…18−0.24843…⋅1.18356…17+0.91397…⋅1.18356…16−0.35197…⋅1.18356…15+0.89652…⋅1.18356…14−0.44594…⋅1.18356…13+0.89273…⋅1.18356…12−0.53284…⋅1.18356…11+0.90071…⋅1.18356…10−0.61470…⋅1.18356…9+0.91896…⋅1.18356…8−0.69325…⋅1.18356…7+0.94632…⋅1.18356…6−0.76991…⋅1.18356…5+0.98192…⋅1.18356…4−0.84592…⋅1.18356…3+1.02507…⋅1.18356…2−0.92231…⋅1.18356…+1.07532…=65.24755…f′(u41)=20⋅1.18356…19−2.51418…⋅1.18356…18+17.05434…⋅1.18356…17−4.22331…⋅1.18356…16+14.62354…⋅1.18356…15−5.27956…⋅1.18356…14+12.55136…⋅1.18356…13−5.79734…⋅1.18356…12+10.71285…⋅1.18356…11−5.86129…⋅1.18356…10+9.00714…⋅1.18356…9−5.53237…⋅1.18356…8+7.35171…⋅1.18356…7−4.85277…⋅1.18356…6+5.67797…⋅1.18356…5−3.84958…⋅1.18356…4+3.92769…⋅1.18356…3−2.53776…⋅1.18356…2+2.05015…⋅1.18356…−0.92231…=949.07332…u42=1.11481…
Δu42=∣1.11481…−1.18356…∣=0.06874…Δu42=0.06874…
u43=1.04579…:Δu43=0.06901…
f(u42)=1.11481…20−0.13232…⋅1.11481…19+0.94746…⋅1.11481…18−0.24843…⋅1.11481…17+0.91397…⋅1.11481…16−0.35197…⋅1.11481…15+0.89652…⋅1.11481…14−0.44594…⋅1.11481…13+0.89273…⋅1.11481…12−0.53284…⋅1.11481…11+0.90071…⋅1.11481…10−0.61470…⋅1.11481…9+0.91896…⋅1.11481…8−0.69325…⋅1.11481…7+0.94632…⋅1.11481…6−0.76991…⋅1.11481…5+0.98192…⋅1.11481…4−0.84592…⋅1.11481…3+1.02507…⋅1.11481…2−0.92231…⋅1.11481…+1.07532…=23.98213…f′(u42)=20⋅1.11481…19−2.51418…⋅1.11481…18+17.05434…⋅1.11481…17−4.22331…⋅1.11481…16+14.62354…⋅1.11481…15−5.27956…⋅1.11481…14+12.55136…⋅1.11481…13−5.79734…⋅1.11481…12+10.71285…⋅1.11481…11−5.86129…⋅1.11481…10+9.00714…⋅1.11481…9−5.53237…⋅1.11481…8+7.35171…⋅1.11481…7−4.85277…⋅1.11481…6+5.67797…⋅1.11481…5−3.84958…⋅1.11481…4+3.92769…⋅1.11481…3−2.53776…⋅1.11481…2+2.05015…⋅1.11481…−0.92231…=347.47933…u43=1.04579…
Δu43=∣1.04579…−1.11481…∣=0.06901…Δu43=0.06901…
No se puede encontrar solución
Las soluciones sonu≈0.90044…,u≈−1.03277…
Las soluciones sonu=−1,u≈0.90044…,u≈−1.03277…
Sustituir en la ecuación u=sin(x)sin(x)=−1,sin(x)≈0.90044…,sin(x)≈−1.03277…
sin(x)=−1,sin(x)≈0.90044…,sin(x)≈−1.03277…
sin(x)=−1:x=23π+2πn
sin(x)=−1
Soluciones generales para sin(x)=−1
tabla de valores periódicos con 2πn intervalos:
x06π4π3π2π32π43π65πsin(x)02122231232221xπ67π45π34π23π35π47π611πsin(x)0−21−22−23−1−23−22−21
x=23π+2πn
x=23π+2πn
sin(x)=0.90044…:x=arcsin(0.90044…)+2πn,x=π−arcsin(0.90044…)+2πn
sin(x)=0.90044…
Aplicar propiedades trigonométricas inversas
sin(x)=0.90044…
Soluciones generales para sin(x)=0.90044…sin(x)=a⇒x=arcsin(a)+2πn,x=π−arcsin(a)+2πnx=arcsin(0.90044…)+2πn,x=π−arcsin(0.90044…)+2πn
x=arcsin(0.90044…)+2πn,x=π−arcsin(0.90044…)+2πn
sin(x)=−1.03277…:Sin solución
sin(x)=−1.03277…
−1≤sin(x)≤1Sinsolucioˊn
Combinar toda las solucionesx=23π+2πn,x=arcsin(0.90044…)+2πn,x=π−arcsin(0.90044…)+2πn
Mostrar soluciones en forma decimalx=23π+2πn,x=1.12079…+2πn,x=π−1.12079…+2πn