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tanh(mL)=0.99

Solución

tanh (m L) = 0.99

Solución

L = \frac{ln ( \frac{1.99}{0.01} )}{2 m}

Pasos de solución

tanh (m L) = 0.99

Re-escribir usando identidades trigonométricas

tanh (m L) = 0.99

Utilizar la identidad hiperbólica:

tanh (x) = \frac{e ^{x} - e ^{- x}}{e ^{x} + e ^{- x}}

\frac{e ^{m L} - e ^{- m L}}{e ^{m L} + e ^{- m L}} = 0.99

\frac{e ^{m L} - e ^{- m L}}{e ^{m L} + e ^{- m L}} = 0.99

\frac{e ^{m L} - e ^{- m L}}{e ^{m L} + e ^{- m L}} = 0.99 : L = \frac{ln ( \frac{1.99}{0.01} )}{2 m} {m < 0 or m > 0}

\frac{e ^{m L} - e ^{- m L}}{e ^{m L} + e ^{- m L}} = 0.99

Multiplicar ambos lados por

e^{m L} + e^{- m L}

\frac{e ^{m L} - e ^{- m L}}{e ^{m L} + e ^{- m L}} (e^{m L} + e^{- m L}) = 0.99 (e^{m L} + e^{- m L})

Simplificar

e^{m L} - e^{- m L} = 0.99 (e^{m L} + e^{- m L})

Restar

0.99 (e^{m L} + e^{- m L})

de ambos lados

e^{m L} - e^{- m L} - 0.99 (e^{m L} + e^{- m L}) = 0.99 (e^{m L} + e^{- m L}) - 0.99 (e^{m L} + e^{- m L})

Simplificar

e^{m L} - e^{- m L} - 0.99 (e^{m L} + e^{- m L}) = 0

Factorizar

e^{m L} - e^{- m L} - 0.99 (e^{m L} + e^{- m L}) : e^{- m L} (0.01 e^{m L} + 1.99) (0.01 e^{m L} - 1.99)

e^{m L} - e^{- m L} - 0.99 (e^{m L} + e^{- m L})

Factorizar

e^{m L} + e^{- m L} : e^{- m L} (e^{2 m L} + 1)

e^{m L} + e^{- m L}

Aplicar las leyes de los exponentes:

a^{b + c} = a^{b} a^{c}

e^{m L} = e^{- m L} e^{2 m L}

= e^{- m L} e^{2 m L} + e^{- m L}

Factorizar el termino común

e^{- m L}

= e^{- m L} (e^{2 m L} + 1)

= e^{m L} - e^{- m L} - 0.99 e^{- m L} (e^{2 m L} + 1)

Aplicar las leyes de los exponentes:

a^{b + c} = a^{b} a^{c}

e^{m L} = e^{- m L} e^{2 m L}

= e^{- m L} e^{2 m L} - e^{- m L} - 0.99 e^{- m L} (e^{2 m L} + 1)

Factorizar el termino común

e^{- m L}

= e^{- m L} (e^{2 m L} - 1 - 0.99 (e^{2 m L} + 1))

Factorizar

e^{2 m L} - 0.99 (e^{2 m L} + 1) - 1 : (0.01 e^{m L} + 1.99) (0.01 e^{m L} - 1.99)

e^{2 m L} - 1 - 0.99 (e^{2 m L} + 1)

Expandir

- 0.99 (e^{2 m L} + 1) : - 0.99 e^{2 m L} - 0.99

- 0.99 (e^{2 m L} + 1)

Poner los parentesis utilizando:

a (b + c) = ab + a c

a = - 0.99, b = e^{2 m L}, c = 1

= - 0.99 e^{2 m L} + (- 0.99) \cdot 1

Aplicar las reglas de los signos

+ (- a) = - a

= - 0.99 e^{2 m L} - 1 \cdot 0.99

Multiplicar los numeros:

1 \cdot 0.99 = 0.99

= - 0.99 e^{2 m L} - 0.99

= e^{2 m L} - 1 - 0.99 e^{2 m L} - 0.99

Simplificar

e^{2 m L} - 1 - 0.99 e^{2 m L} - 0.99 : 0.01 e^{2 m L} - 1.99

e^{2 m L} - 1 - 0.99 e^{2 m L} - 0.99

Agrupar términos semejantes

= e^{2 m L} - 0.99 e^{2 m L} - 1 - 0.99

Sumar elementos similares:

e^{2 m L} - 0.99 e^{2 m L} = 0.01 e^{2 m L}

= 0.01 e^{2 m L} - 1 - 0.99

Restar:

- 1 - 0.99 = - 1.99

= 0.01 e^{2 m L} - 1.99

= 0.01 e^{2 m L} - 1.99

Aplicar las leyes de los exponentes:

a^{b c} = (a^{b})^{c}

e^{2 m L} = (e^{m L})^{2}

= 0.01 (e^{m L})^{2} - 1.99

Reescribir

0.01 (e^{m L})^{2} - 1.99

como

(0.01 e^{m L})^{2} - (1.99)^{2}

0.01 (e^{m L})^{2} - 1.99

Aplicar las leyes de los exponentes:

a = (a)^{2}

0.01 = (0.01)^{2}

= (0.01)^{2} (e^{m L})^{2} - 1.99

Aplicar las leyes de los exponentes:

a = (a)^{2}

1.99 = (1.99)^{2}

= (0.01)^{2} (e^{m L})^{2} - (1.99)^{2}

Aplicar las leyes de los exponentes:

a^{m} b^{m} = (ab)^{m}

(0.01)^{2} (e^{m L})^{2} = (0.01 e^{m L})^{2}

= (0.01 e^{m L})^{2} - (1.99)^{2}

= (0.01 e^{m L})^{2} - (1.99)^{2}

Aplicar la siguiente regla para binomios al cuadrado:

x^{2} - y^{2} = (x + y) (x - y)

(0.01 e^{m L})^{2} - (1.99)^{2} = (0.01 e^{m L} + 1.99) (0.01 e^{m L} - 1.99)

= (0.01 e^{m L} + 1.99) (0.01 e^{m L} - 1.99)

= e^{- m L} (0.01 e^{m L} + 1.99) (0.01 e^{m L} - 1.99)

e^{- m L} (0.01 e^{m L} + 1.99) (0.01 e^{m L} - 1.99) = 0

Utilizando el teorema de factor cero: si

ab = 0

entonces

a = 0

b = 0

e^{- m L} = 0 or 0.01 e^{m L} + 1.99 = 0 or 0.01 e^{m L} - 1.99 = 0

Resolver

e^{- m L} = 0 :

Sin solución para

L \in R

e^{- m L} = 0

a^{f (L)}

no puede ser cero o negativo para

L \in R

Sin soluci \overset{o}{ˊ} n para L \in R

Resolver

0.01 e^{m L} + 1.99 = 0 :

Sin solución para

L \in R

0.01 e^{m L} + 1.99 = 0

Restar

1.99

de ambos lados

0.01 e^{m L} + 1.99 - 1.99 = 0 - 1.99

Simplificar

0.01 e^{m L} = - 1.99

Dividir ambos lados entre

0.01

0.01 e^{m L} = - 1.99

Dividir ambos lados entre

0.01

\frac{0.01 e ^{m L}}{0.01} = \frac{- 1.99}{0.01}

Simplificar

e^{m L} = - \frac{1.99}{0.01}

e^{m L} = - \frac{1.99}{0.01}

Simplificar

e^{m L} = - \frac{1.99}{0.01}

a^{f (L)}

no puede ser cero o negativo para

L \in R

Sin soluci \overset{o}{ˊ} n para L \in R

Resolver

0.01 e^{m L} - 1.99 = 0 : L = \frac{ln ( \frac{1.99}{0.01} )}{2 m}

0.01 e^{m L} - 1.99 = 0

Sumar

1.99

a ambos lados

0.01 e^{m L} - 1.99 + 1.99 = 0 + 1.99

Simplificar

0.01 e^{m L} = 1.99

Dividir ambos lados entre

0.01

0.01 e^{m L} = 1.99

Dividir ambos lados entre

0.01

\frac{0.01 e ^{m L}}{0.01} = \frac{1.99}{0.01}

Simplificar

e^{m L} = \frac{1.99}{0.01}

e^{m L} = \frac{1.99}{0.01}

Simplificar

e^{m L} = \frac{1.99}{0.01}

Aplicar las leyes de los exponentes

e^{m L} = \frac{1.99}{0.01}

Aplicar las leyes de los exponentes:

a = a^{\frac{1}{2}}

\frac{1.99}{0.01} = (\frac{1.99}{0.01})^{\frac{1}{2}}

e^{m L} = (\frac{1.99}{0.01})^{\frac{1}{2}}

f (x) = g (x)

, entonces

ln (f (x)) = ln (g (x))

ln (e^{m L}) = ln ((\frac{1.99}{0.01})^{\frac{1}{2}})

Aplicar las propiedades de los logaritmos:

ln (e^{a}) = a

ln (e^{m L}) = m L

m L = ln ((\frac{1.99}{0.01})^{\frac{1}{2}})

Aplicar las propiedades de los logaritmos:

ln (x^{a}) = a \cdot ln (x)

ln ((\frac{1.99}{0.01})^{\frac{1}{2}}) = \frac{1}{2} ln (\frac{1.99}{0.01})

m L = \frac{1}{2} ln (\frac{1.99}{0.01})

m L = \frac{1}{2} ln (\frac{1.99}{0.01})

Resolver

m L = \frac{1}{2} ln (\frac{1.99}{0.01}) : L = \frac{ln ( \frac{1.99}{0.01} )}{2 m}

m L = \frac{1}{2} ln (\frac{1.99}{0.01})

Dividir ambos lados entre

m

m L = \frac{1}{2} ln (\frac{1.99}{0.01})

Dividir ambos lados entre

m

\frac{m L}{m} = \frac{\frac{1}{2} ln ( \frac{1.99}{0.01} )}{m}

Simplificar

\frac{m L}{m} = \frac{\frac{1}{2} ln ( \frac{1.99}{0.01} )}{m}

Simplificar

\frac{m L}{m} : L

\frac{m L}{m}

Eliminar los terminos comunes:

m

= L

Simplificar

\frac{\frac{1}{2} ln ( \frac{1.99}{0.01} )}{m} : \frac{ln ( \frac{1.99}{0.01} )}{2 m}

\frac{\frac{1}{2} ln ( \frac{1.99}{0.01} )}{m}

Multiplicar

\frac{1}{2} ln (\frac{1.99}{0.01}) : \frac{ln ( \frac{1.99}{0.01} )}{2}

\frac{1}{2} ln (\frac{1.99}{0.01})

Multiplicar fracciones:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot ln ( \frac{1.99}{0.01} )}{2}

Multiplicar:

1 \cdot ln (\frac{1.99}{0.01}) = ln (\frac{1.99}{0.01})

= \frac{ln ( \frac{1.99}{0.01} )}{2}

= \frac{\frac{l n ( \frac{1.99}{0.01} )}{2}}{m}

Aplicar las propiedades de las fracciones:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{ln ( \frac{1.99}{0.01} )}{2 m}

L = \frac{ln ( \frac{1.99}{0.01} )}{2 m}

L = \frac{ln ( \frac{1.99}{0.01} )}{2 m}

L = \frac{ln ( \frac{1.99}{0.01} )}{2 m}

L = \frac{ln ( \frac{1.99}{0.01} )}{2 m}

Verificar las soluciones:

L = \frac{ln ( \frac{1.99}{0.01} )}{2 m} {m < 0 or m > 0}

Verificar las soluciones sustituyéndolas en

\frac{e ^{m L} - e ^{- m L}}{e ^{m L} + e ^{- m L}} = 0.99

Quitar las que no concuerden con la ecuación.

Sustituir

L = \frac{ln ( \frac{1.99}{0.01} )}{2 m} : m < 0 or m > 0

\frac{e ^{m (\frac{l n ( \frac{1.99}{0.01} )}{2 m})} - e ^{- m (\frac{l n ( \frac{1.99}{0.01} )}{2 m})}}{e ^{m (\frac{l n ( \frac{1.99}{0.01} )}{2 m})} + e ^{- m (\frac{l n ( \frac{1.99}{0.01} )}{2 m})}} = 0.99

\frac{e ^{m (\frac{l n ( \frac{1.99}{0.01} )}{2 m})} - e ^{- m (\frac{l n ( \frac{1.99}{0.01} )}{2 m})}}{e ^{m (\frac{l n ( \frac{1.99}{0.01} )}{2 m})} + e ^{- m (\frac{l n ( \frac{1.99}{0.01} )}{2 m})}} = 0.99

\frac{e ^{m (\frac{l n ( \frac{1.99}{0.01} )}{2 m})} - e ^{- m (\frac{l n ( \frac{1.99}{0.01} )}{2 m})}}{e ^{m (\frac{l n ( \frac{1.99}{0.01} )}{2 m})} + e ^{- m (\frac{l n ( \frac{1.99}{0.01} )}{2 m})}}

Quitar los parentesis:

(a) = a

= \frac{e ^{m \frac{l n ( \frac{1.99}{0.01} )}{2 m}} - e ^{- m \frac{l n ( \frac{1.99}{0.01} )}{2 m}}}{e ^{m \frac{l n ( \frac{1.99}{0.01} )}{2 m}} + e ^{- m \frac{l n ( \frac{1.99}{0.01} )}{2 m}}}

Multiplicar

m \frac{ln ( \frac{1.99}{0.01} )}{2 m} : 2.64665 \dots

m \frac{ln ( \frac{1.99}{0.01} )}{2 m}

Multiplicar fracciones:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{ln ( \frac{1.99}{0.01} ) m}{2 m}

Eliminar los terminos comunes:

m

= \frac{ln ( \frac{1.99}{0.01} )}{2}

Convertir el elemento a una forma decimal

\frac{1}{2} = 0.5

= 0.5 ln (\frac{1.99}{0.01})

Dividir:

\frac{1.99}{0.01} = 199

= 0.5 ln (199)

Simplificar

ln (199) : 5.29330 \dots

ln (199)

Simplificar a una forma decimal

= 5.29330 \dots

= 0.5 \cdot 5.29330 \dots

Multiplicar los numeros:

0.5 \cdot 5.29330 \dots = 2.64665 \dots

= 2.64665 \dots

= \frac{e ^{m \frac{l n ( \frac{1.99}{0.01} )}{2 m}} - e ^{- m \frac{l n ( \frac{1.99}{0.01} )}{2 m}}}{e ^{2.64665 \dots} + e ^{- m \frac{l n ( \frac{1.99}{0.01} )}{2 m}}}

Multiplicar

- m \frac{ln ( \frac{1.99}{0.01} )}{2 m} : - 2.64665 \dots

- m \frac{ln ( \frac{1.99}{0.01} )}{2 m}

Multiplicar fracciones:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{ln ( \frac{1.99}{0.01} ) m}{2 m}

Eliminar los terminos comunes:

m

= - \frac{ln ( \frac{1.99}{0.01} )}{2}

Convertir el elemento a una forma decimal

\frac{1}{2} = 0.5

= - 0.5 ln (\frac{1.99}{0.01})

Dividir:

\frac{1.99}{0.01} = 199

= - 0.5 ln (199)

Simplificar

ln (199) : 5.29330 \dots

ln (199)

Simplificar a una forma decimal

= 5.29330 \dots

= - 0.5 \cdot 5.29330 \dots

Multiplicar los numeros:

0.5 \cdot 5.29330 \dots = 2.64665 \dots

= - 2.64665 \dots

= \frac{e ^{m \frac{l n ( \frac{1.99}{0.01} )}{2 m}} - e ^{- m \frac{l n ( \frac{1.99}{0.01} )}{2 m}}}{e ^{2.64665 \dots} + e ^{- 2.64665 \dots}}

Multiplicar

m \frac{ln ( \frac{1.99}{0.01} )}{2 m} : 2.64665 \dots

m \frac{ln ( \frac{1.99}{0.01} )}{2 m}

Multiplicar fracciones:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{ln ( \frac{1.99}{0.01} ) m}{2 m}

Eliminar los terminos comunes:

m

= \frac{ln ( \frac{1.99}{0.01} )}{2}

Convertir el elemento a una forma decimal

\frac{1}{2} = 0.5

= 0.5 ln (\frac{1.99}{0.01})

Dividir:

\frac{1.99}{0.01} = 199

= 0.5 ln (199)

Simplificar

ln (199) : 5.29330 \dots

ln (199)

Simplificar a una forma decimal

= 5.29330 \dots

= 0.5 \cdot 5.29330 \dots

Multiplicar los numeros:

0.5 \cdot 5.29330 \dots = 2.64665 \dots

= 2.64665 \dots

= \frac{e ^{2.64665 \dots} - e ^{- m \frac{l n ( \frac{1.99}{0.01} )}{2 m}}}{e ^{2.64665 \dots} + e ^{- 2.64665 \dots}}

Multiplicar

- m \frac{ln ( \frac{1.99}{0.01} )}{2 m} : - 2.64665 \dots

- m \frac{ln ( \frac{1.99}{0.01} )}{2 m}

Multiplicar fracciones:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{ln ( \frac{1.99}{0.01} ) m}{2 m}

Eliminar los terminos comunes:

m

= - \frac{ln ( \frac{1.99}{0.01} )}{2}

Convertir el elemento a una forma decimal

\frac{1}{2} = 0.5

= - 0.5 ln (\frac{1.99}{0.01})

Dividir:

\frac{1.99}{0.01} = 199

= - 0.5 ln (199)

Simplificar

ln (199) : 5.29330 \dots

ln (199)

Simplificar a una forma decimal

= 5.29330 \dots

= - 0.5 \cdot 5.29330 \dots

Multiplicar los numeros:

0.5 \cdot 5.29330 \dots = 2.64665 \dots

= - 2.64665 \dots

= \frac{e ^{2.64665 \dots} - e ^{- 2.64665 \dots}}{e ^{2.64665 \dots} + e ^{- 2.64665 \dots}}

Simplificar

\frac{e ^{2.64665 \dots} - e ^{- 2.64665 \dots}}{e ^{2.64665 \dots} + e ^{- 2.64665 \dots}}

Aplicar las leyes de los exponentes:

a^{- b} = \frac{1}{a ^{b}}

e^{- 2.64665 \dots} = \frac{1}{e ^{2.64665 \dots}}

= \frac{e ^{2.64665 \dots} - e ^{- 2.64665 \dots}}{e ^{2.64665 \dots} + \frac{1}{e ^{2.64665 \dots}}}

Aplicar las leyes de los exponentes:

a^{- b} = \frac{1}{a ^{b}}

e^{- 2.64665 \dots} = \frac{1}{e ^{2.64665 \dots}}

= \frac{e ^{2.64665 \dots} - \frac{1}{e ^{2.64665 \dots}}}{e ^{2.64665 \dots} + \frac{1}{e ^{2.64665 \dots}}}

Simplificar

e^{2.64665 \dots} + \frac{1}{e ^{2.64665 \dots}}

en una fracción:

14.17762 \dots

e^{2.64665 \dots} + \frac{1}{e ^{2.64665 \dots}}

Convertir a fracción:

e^{2.64665 \dots} = \frac{e ^{2.64665 \dots} e ^{2.64665 \dots}}{e ^{2.64665 \dots}}

= \frac{e ^{2.64665 \dots} e ^{2.64665 \dots}}{e ^{2.64665 \dots}} + \frac{1}{e ^{2.64665 \dots}}

Ya que los denominadores son iguales, combinar las fracciones:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{e ^{2.64665 \dots} e ^{2.64665 \dots} + 1}{e ^{2.64665 \dots}}

e^{2.64665 \dots} e^{2.64665 \dots} + 1 = e^{5.29330 \dots} + 1

e^{2.64665 \dots} e^{2.64665 \dots} + 1

e^{2.64665 \dots} e^{2.64665 \dots} = e^{5.29330 \dots}

e^{2.64665 \dots} e^{2.64665 \dots}

Aplicar las leyes de los exponentes:

a^{b} \cdot a^{c} = a^{b + c}

e^{2.64665 \dots} e^{2.64665 \dots} = e^{2.64665 \dots + 2.64665 \dots}

= e^{2.64665 \dots + 2.64665 \dots}

Sumar:

2.64665 \dots + 2.64665 \dots = 5.29330 \dots

= e^{5.29330 \dots}

= e^{5.29330 \dots} + 1

= \frac{e ^{5.29330 \dots} + 1}{e ^{2.64665 \dots}}

e^{5.29330 \dots} = 198.99999 \dots

= \frac{198.99999 \dots + 1}{e ^{2.64665 \dots}}

Sumar:

198.99999 \dots + 1 = 199.99999 \dots

= \frac{199.99999 \dots}{e ^{2.64665 \dots}}

e^{2.64665 \dots} = 14.10673 \dots

= \frac{199.99999 \dots}{14.10673 \dots}

Dividir:

\frac{199.99999 \dots}{14.10673 \dots} = 14.17762 \dots

= 14.17762 \dots

= \frac{e ^{2.64665 \dots} - \frac{1}{e ^{2.64665 \dots}}}{14.17762 \dots}

Simplificar

e^{2.64665 \dots} - \frac{1}{e ^{2.64665 \dots}}

en una fracción:

14.03584 \dots

e^{2.64665 \dots} - \frac{1}{e ^{2.64665 \dots}}

Convertir a fracción:

e^{2.64665 \dots} = \frac{e ^{2.64665 \dots} e ^{2.64665 \dots}}{e ^{2.64665 \dots}}

= \frac{e ^{2.64665 \dots} e ^{2.64665 \dots}}{e ^{2.64665 \dots}} - \frac{1}{e ^{2.64665 \dots}}

Ya que los denominadores son iguales, combinar las fracciones:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{e ^{2.64665 \dots} e ^{2.64665 \dots} - 1}{e ^{2.64665 \dots}}

e^{2.64665 \dots} e^{2.64665 \dots} - 1 = e^{5.29330 \dots} - 1

e^{2.64665 \dots} e^{2.64665 \dots} - 1

e^{2.64665 \dots} e^{2.64665 \dots} = e^{5.29330 \dots}

e^{2.64665 \dots} e^{2.64665 \dots}

Aplicar las leyes de los exponentes:

a^{b} \cdot a^{c} = a^{b + c}

e^{2.64665 \dots} e^{2.64665 \dots} = e^{2.64665 \dots + 2.64665 \dots}

= e^{2.64665 \dots + 2.64665 \dots}

Sumar:

2.64665 \dots + 2.64665 \dots = 5.29330 \dots

= e^{5.29330 \dots}

= e^{5.29330 \dots} - 1

= \frac{e ^{5.29330 \dots} - 1}{e ^{2.64665 \dots}}

e^{5.29330 \dots} = 198.99999 \dots

= \frac{198.99999 \dots - 1}{e ^{2.64665 \dots}}

Restar:

198.99999 \dots - 1 = 197.99999 \dots

= \frac{197.99999 \dots}{e ^{2.64665 \dots}}

e^{2.64665 \dots} = 14.10673 \dots

= \frac{197.99999 \dots}{14.10673 \dots}

Dividir:

\frac{197.99999 \dots}{14.10673 \dots} = 14.03584 \dots

= 14.03584 \dots

= \frac{14.03584 \dots}{14.17762 \dots}

Dividir:

\frac{14.03584 \dots}{14.17762 \dots} = 0.99

= 0.99

= 0.99

0.99 = 0.99

Dominio de

\frac{e ^{m (\frac{l n ( \frac{1.99}{0.01} )}{2 m})} - e ^{- m (\frac{l n ( \frac{1.99}{0.01} )}{2 m})}}{e ^{m (\frac{l n ( \frac{1.99}{0.01} )}{2 m})} + e ^{- m (\frac{l n ( \frac{1.99}{0.01} )}{2 m})}} : m < 0 or m > 0

Definición de dominio

Encontrar los puntos no definidos (singularidades):

m = 0

\frac{e ^{m (\frac{l n ( \frac{1.99}{0.01} )}{2 m})} - e ^{- m (\frac{l n ( \frac{1.99}{0.01} )}{2 m})}}{e ^{m (\frac{l n ( \frac{1.99}{0.01} )}{2 m})} + e ^{- m (\frac{l n ( \frac{1.99}{0.01} )}{2 m})}}

Tomar el(los) denominador(es) de

\frac{e ^{m (\frac{l n ( \frac{1.99}{0.01} )}{2 m})} - e ^{- m (\frac{l n ( \frac{1.99}{0.01} )}{2 m})}}{e ^{m (\frac{l n ( \frac{1.99}{0.01} )}{2 m})} + e ^{- m (\frac{l n ( \frac{1.99}{0.01} )}{2 m})}}

y comparar con cero

Resolver

2 m = 0 : m = 0

2 m = 0

Dividir ambos lados entre

2

2 m = 0

Dividir ambos lados entre

2

\frac{2 m}{2} = \frac{0}{2}

Simplificar

m = 0

m = 0

Los siguientes puntos no están definidos

m = 0

El dominio de la función

m < 0 or m > 0

m < 0 or m > 0

La solución es

L = \frac{ln ( \frac{1.99}{0.01} )}{2 m} {m < 0 or m > 0}

L = \frac{ln ( \frac{1.99}{0.01} )}{2 m}

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