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- Límite de la función:
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Límite de (5-x^2+2*x^3+3*x^4+5*x)/(1+x^3)
-
Límite de 3*asin(x)/(4*x)
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Límite de (1-2*x+2*x^3)/(2+3*x^2+4*x)
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Límite de (-16+2^x)/(-1+5*sqrt(x)*(5-x))
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Expresiones idénticas
- log(uno +x)/(asin(setenta y siete *sqrt(x))*sqrt(tan(setenta *x)))
- logaritmo de (1 más x) dividir por ( ar coseno de eno de (77 multiplicar por raíz cuadrada de (x)) multiplicar por raíz cuadrada de ( tangente de (70 multiplicar por x)))
- logaritmo de (uno más x) dividir por ( ar coseno de eno de (setenta y siete multiplicar por raíz cuadrada de (x)) multiplicar por raíz cuadrada de ( tangente de (setenta multiplicar por x)))
- log(1+x)/(asin(77*√(x))*√(tan(70*x)))
- log(1+x)/(asin(77sqrt(x))sqrt(tan(70x)))
- log1+x/asin77sqrtxsqrttan70x
- log(1+x) dividir por (asin(77*sqrt(x))*sqrt(tan(70*x)))
-
Expresiones semejantes
- log(1-x)/(asin(77*sqrt(x))*sqrt(tan(70*x)))
- log(1+x)/(arcsin(77*sqrt(x))*sqrt(tan(70*x)))
-
Expresiones con funciones
- Logaritmo log
- log(x)/(1-log(x))
- log(x)/(z*(1+z^2))
- log((5+3*x)/(-4+3*x))^2
- log(7+x^2-4*x)/2-log(33)/2-pi*i/2+2*sqrt(3)*atan(2*sqrt(3)/3)/3+2*sqrt(3)*atan(sqrt(3)*(-2+x)/3)/3
- log(-1+x^2)/(1+x^2)
- Arcoseno arcsin
- asin(2*x)/(-1+log(-1+e))
- asin(x+sqrt(x+x^2))
- Raíz cuadrada sqrt
- sqrt(x*(-6+x))-x
- sqrt(-7+t)
- sqrt(7+x^2+4*x)-sqrt(1+x^2-5*x)
- sqrt(8+x)-sqrt(8-x)
- sqrt(4+x^4)-sqrt(2+x^4-6*x^2)
- Raíz cuadrada sqrt
- sqrt(x*(-6+x))-x
- sqrt(-7+t)
- sqrt(7+x^2+4*x)-sqrt(1+x^2-5*x)
- sqrt(8+x)-sqrt(8-x)
- sqrt(4+x^4)-sqrt(2+x^4-6*x^2)
- Tangente tan
- tan(6*x)^3*cos(7*x)/(asin(x)^2*sin(3*x))
- tan(x)*tan(3*x)
- tan(-3+3^(pi/x))
- tan(3*x)^3/(2*x*sin(x)^2)
- tan(5*x)^3/(2*sin(7*x))
Límite de la función log(1+x)/(asin(77*sqrt(x))*sqrt(tan(70*x)))
Solución
Ha introducido
[src]
/ log(1 + x) \
lim |----------------------------|
x->0+| / ___\ ___________|
\asin\77*\/ x /*\/ tan(70*x) /
$$\lim_{x \to 0^+}\left(\frac{\log{\left(x + 1 \right)}}{\sqrt{\tan{\left(70 x \right)}} \operatorname{asin}{\left(77 \sqrt{x} \right)}}\right)$$
Limit(log(1 + x)/((asin(77*sqrt(x))*sqrt(tan(70*x)))), x, 0)
Método de l'Hopital
Tenemos la indeterminación de tipo
tal que el límite para el numerador es
$$\lim_{x \to 0^+}\left(\frac{\log{\left(x + 1 \right)}}{\sqrt{\tan{\left(70 x \right)}}}\right) = 0$$
y el límite para el denominador es
$$\lim_{x \to 0^+} \operatorname{asin}{\left(77 \sqrt{x} \right)} = 0$$
Vamos a probar las derivadas del numerador y denominador hasta eliminar la indeterminación.
$$\lim_{x \to 0^+}\left(\frac{\log{\left(x + 1 \right)}}{\sqrt{\tan{\left(70 x \right)}} \operatorname{asin}{\left(77 \sqrt{x} \right)}}\right)$$
=
Introducimos una pequeña modificación de la función bajo el signo del límite
$$\lim_{x \to 0^+}\left(\frac{\log{\left(x + 1 \right)}}{\sqrt{\tan{\left(70 x \right)}} \operatorname{asin}{\left(77 \sqrt{x} \right)}}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{\frac{d}{d x} \frac{\log{\left(x + 1 \right)}}{\sqrt{\tan{\left(70 x \right)}}}}{\frac{d}{d x} \operatorname{asin}{\left(77 \sqrt{x} \right)}}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{2 \sqrt{x} \sqrt{1 - 5929 x} \left(\frac{\left(- 35 \tan^{2}{\left(70 x \right)} - 35\right) \log{\left(x + 1 \right)}}{\tan^{\frac{3}{2}}{\left(70 x \right)}} + \frac{1}{\left(x + 1\right) \sqrt{\tan{\left(70 x \right)}}}\right)}{77}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{2 \sqrt{x} \left(\frac{\left(- 35 \tan^{2}{\left(70 x \right)} - 35\right) \log{\left(x + 1 \right)}}{\tan^{\frac{3}{2}}{\left(70 x \right)}} + \frac{1}{\left(x + 1\right) \sqrt{\tan{\left(70 x \right)}}}\right)}{77}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{\frac{d}{d x} \frac{2 \sqrt{x}}{77}}{\frac{d}{d x} \frac{1}{\frac{\left(- 35 \tan^{2}{\left(70 x \right)} - 35\right) \log{\left(x + 1 \right)}}{\tan^{\frac{3}{2}}{\left(70 x \right)}} + \frac{1}{\left(x + 1\right) \sqrt{\tan{\left(70 x \right)}}}}}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{1225 \log{\left(x + 1 \right)}^{2} \tan{\left(70 x \right)} + \frac{2450 \log{\left(x + 1 \right)}^{2}}{\tan{\left(70 x \right)}} + \frac{1225 \log{\left(x + 1 \right)}^{2}}{\tan^{3}{\left(70 x \right)}} + \frac{1}{x^{2} \tan{\left(70 x \right)} + 2 x \tan{\left(70 x \right)} + \tan{\left(70 x \right)}} - \frac{70 \log{\left(x + 1 \right)} \tan^{2}{\left(70 x \right)}}{x \tan^{2}{\left(70 x \right)} + \tan^{2}{\left(70 x \right)}} - \frac{70 \log{\left(x + 1 \right)}}{x \tan^{2}{\left(70 x \right)} + \tan^{2}{\left(70 x \right)}}}{77 \sqrt{x} \left(1225 \log{\left(x + 1 \right)} \tan^{\frac{3}{2}}{\left(70 x \right)} - \frac{2450 \log{\left(x + 1 \right)}}{\sqrt{\tan{\left(70 x \right)}}} - \frac{3675 \log{\left(x + 1 \right)}}{\tan^{\frac{5}{2}}{\left(70 x \right)}} + \frac{1}{x^{2} \sqrt{\tan{\left(70 x \right)}} + 2 x \sqrt{\tan{\left(70 x \right)}} + \sqrt{\tan{\left(70 x \right)}}} + \frac{70 \tan^{2}{\left(70 x \right)}}{x \tan^{\frac{3}{2}}{\left(70 x \right)} + \tan^{\frac{3}{2}}{\left(70 x \right)}} + \frac{70}{x \tan^{\frac{3}{2}}{\left(70 x \right)} + \tan^{\frac{3}{2}}{\left(70 x \right)}}\right)}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{1225 \log{\left(x + 1 \right)}^{2} \tan{\left(70 x \right)} + \frac{2450 \log{\left(x + 1 \right)}^{2}}{\tan{\left(70 x \right)}} + \frac{1225 \log{\left(x + 1 \right)}^{2}}{\tan^{3}{\left(70 x \right)}} + \frac{1}{x^{2} \tan{\left(70 x \right)} + 2 x \tan{\left(70 x \right)} + \tan{\left(70 x \right)}} - \frac{70 \log{\left(x + 1 \right)} \tan^{2}{\left(70 x \right)}}{x \tan^{2}{\left(70 x \right)} + \tan^{2}{\left(70 x \right)}} - \frac{70 \log{\left(x + 1 \right)}}{x \tan^{2}{\left(70 x \right)} + \tan^{2}{\left(70 x \right)}}}{77 \sqrt{x} \left(1225 \log{\left(x + 1 \right)} \tan^{\frac{3}{2}}{\left(70 x \right)} - \frac{2450 \log{\left(x + 1 \right)}}{\sqrt{\tan{\left(70 x \right)}}} - \frac{3675 \log{\left(x + 1 \right)}}{\tan^{\frac{5}{2}}{\left(70 x \right)}} + \frac{1}{x^{2} \sqrt{\tan{\left(70 x \right)}} + 2 x \sqrt{\tan{\left(70 x \right)}} + \sqrt{\tan{\left(70 x \right)}}} + \frac{70 \tan^{2}{\left(70 x \right)}}{x \tan^{\frac{3}{2}}{\left(70 x \right)} + \tan^{\frac{3}{2}}{\left(70 x \right)}} + \frac{70}{x \tan^{\frac{3}{2}}{\left(70 x \right)} + \tan^{\frac{3}{2}}{\left(70 x \right)}}\right)}\right)$$
=
$$\frac{\sqrt{70}}{5390}$$
Como puedes ver, hemos aplicado el método de l'Hopital (utilizando la derivada del numerador y denominador) 2 vez (veces)
0/0,
tal que el límite para el numerador es
$$\lim_{x \to 0^+}\left(\frac{\log{\left(x + 1 \right)}}{\sqrt{\tan{\left(70 x \right)}}}\right) = 0$$
y el límite para el denominador es
$$\lim_{x \to 0^+} \operatorname{asin}{\left(77 \sqrt{x} \right)} = 0$$
Vamos a probar las derivadas del numerador y denominador hasta eliminar la indeterminación.
$$\lim_{x \to 0^+}\left(\frac{\log{\left(x + 1 \right)}}{\sqrt{\tan{\left(70 x \right)}} \operatorname{asin}{\left(77 \sqrt{x} \right)}}\right)$$
=
Introducimos una pequeña modificación de la función bajo el signo del límite
$$\lim_{x \to 0^+}\left(\frac{\log{\left(x + 1 \right)}}{\sqrt{\tan{\left(70 x \right)}} \operatorname{asin}{\left(77 \sqrt{x} \right)}}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{\frac{d}{d x} \frac{\log{\left(x + 1 \right)}}{\sqrt{\tan{\left(70 x \right)}}}}{\frac{d}{d x} \operatorname{asin}{\left(77 \sqrt{x} \right)}}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{2 \sqrt{x} \sqrt{1 - 5929 x} \left(\frac{\left(- 35 \tan^{2}{\left(70 x \right)} - 35\right) \log{\left(x + 1 \right)}}{\tan^{\frac{3}{2}}{\left(70 x \right)}} + \frac{1}{\left(x + 1\right) \sqrt{\tan{\left(70 x \right)}}}\right)}{77}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{2 \sqrt{x} \left(\frac{\left(- 35 \tan^{2}{\left(70 x \right)} - 35\right) \log{\left(x + 1 \right)}}{\tan^{\frac{3}{2}}{\left(70 x \right)}} + \frac{1}{\left(x + 1\right) \sqrt{\tan{\left(70 x \right)}}}\right)}{77}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{\frac{d}{d x} \frac{2 \sqrt{x}}{77}}{\frac{d}{d x} \frac{1}{\frac{\left(- 35 \tan^{2}{\left(70 x \right)} - 35\right) \log{\left(x + 1 \right)}}{\tan^{\frac{3}{2}}{\left(70 x \right)}} + \frac{1}{\left(x + 1\right) \sqrt{\tan{\left(70 x \right)}}}}}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{1225 \log{\left(x + 1 \right)}^{2} \tan{\left(70 x \right)} + \frac{2450 \log{\left(x + 1 \right)}^{2}}{\tan{\left(70 x \right)}} + \frac{1225 \log{\left(x + 1 \right)}^{2}}{\tan^{3}{\left(70 x \right)}} + \frac{1}{x^{2} \tan{\left(70 x \right)} + 2 x \tan{\left(70 x \right)} + \tan{\left(70 x \right)}} - \frac{70 \log{\left(x + 1 \right)} \tan^{2}{\left(70 x \right)}}{x \tan^{2}{\left(70 x \right)} + \tan^{2}{\left(70 x \right)}} - \frac{70 \log{\left(x + 1 \right)}}{x \tan^{2}{\left(70 x \right)} + \tan^{2}{\left(70 x \right)}}}{77 \sqrt{x} \left(1225 \log{\left(x + 1 \right)} \tan^{\frac{3}{2}}{\left(70 x \right)} - \frac{2450 \log{\left(x + 1 \right)}}{\sqrt{\tan{\left(70 x \right)}}} - \frac{3675 \log{\left(x + 1 \right)}}{\tan^{\frac{5}{2}}{\left(70 x \right)}} + \frac{1}{x^{2} \sqrt{\tan{\left(70 x \right)}} + 2 x \sqrt{\tan{\left(70 x \right)}} + \sqrt{\tan{\left(70 x \right)}}} + \frac{70 \tan^{2}{\left(70 x \right)}}{x \tan^{\frac{3}{2}}{\left(70 x \right)} + \tan^{\frac{3}{2}}{\left(70 x \right)}} + \frac{70}{x \tan^{\frac{3}{2}}{\left(70 x \right)} + \tan^{\frac{3}{2}}{\left(70 x \right)}}\right)}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{1225 \log{\left(x + 1 \right)}^{2} \tan{\left(70 x \right)} + \frac{2450 \log{\left(x + 1 \right)}^{2}}{\tan{\left(70 x \right)}} + \frac{1225 \log{\left(x + 1 \right)}^{2}}{\tan^{3}{\left(70 x \right)}} + \frac{1}{x^{2} \tan{\left(70 x \right)} + 2 x \tan{\left(70 x \right)} + \tan{\left(70 x \right)}} - \frac{70 \log{\left(x + 1 \right)} \tan^{2}{\left(70 x \right)}}{x \tan^{2}{\left(70 x \right)} + \tan^{2}{\left(70 x \right)}} - \frac{70 \log{\left(x + 1 \right)}}{x \tan^{2}{\left(70 x \right)} + \tan^{2}{\left(70 x \right)}}}{77 \sqrt{x} \left(1225 \log{\left(x + 1 \right)} \tan^{\frac{3}{2}}{\left(70 x \right)} - \frac{2450 \log{\left(x + 1 \right)}}{\sqrt{\tan{\left(70 x \right)}}} - \frac{3675 \log{\left(x + 1 \right)}}{\tan^{\frac{5}{2}}{\left(70 x \right)}} + \frac{1}{x^{2} \sqrt{\tan{\left(70 x \right)}} + 2 x \sqrt{\tan{\left(70 x \right)}} + \sqrt{\tan{\left(70 x \right)}}} + \frac{70 \tan^{2}{\left(70 x \right)}}{x \tan^{\frac{3}{2}}{\left(70 x \right)} + \tan^{\frac{3}{2}}{\left(70 x \right)}} + \frac{70}{x \tan^{\frac{3}{2}}{\left(70 x \right)} + \tan^{\frac{3}{2}}{\left(70 x \right)}}\right)}\right)$$
=
$$\frac{\sqrt{70}}{5390}$$
Como puedes ver, hemos aplicado el método de l'Hopital (utilizando la derivada del numerador y denominador) 2 vez (veces)
Gráfica
Otros límites con x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{\log{\left(x + 1 \right)}}{\sqrt{\tan{\left(70 x \right)}} \operatorname{asin}{\left(77 \sqrt{x} \right)}}\right) = \frac{\sqrt{70}}{5390}$$
Más detalles con x→0 a la izquierda
$$\lim_{x \to 0^+}\left(\frac{\log{\left(x + 1 \right)}}{\sqrt{\tan{\left(70 x \right)}} \operatorname{asin}{\left(77 \sqrt{x} \right)}}\right) = \frac{\sqrt{70}}{5390}$$
$$\lim_{x \to \infty}\left(\frac{\log{\left(x + 1 \right)}}{\sqrt{\tan{\left(70 x \right)}} \operatorname{asin}{\left(77 \sqrt{x} \right)}}\right)$$
Más detalles con x→oo
$$\lim_{x \to 1^-}\left(\frac{\log{\left(x + 1 \right)}}{\sqrt{\tan{\left(70 x \right)}} \operatorname{asin}{\left(77 \sqrt{x} \right)}}\right) = \frac{\log{\left(2 \right)}}{\sqrt{\tan{\left(70 \right)}} \operatorname{asin}{\left(77 \right)}}$$
Más detalles con x→1 a la izquierda
$$\lim_{x \to 1^+}\left(\frac{\log{\left(x + 1 \right)}}{\sqrt{\tan{\left(70 x \right)}} \operatorname{asin}{\left(77 \sqrt{x} \right)}}\right) = \frac{\log{\left(2 \right)}}{\sqrt{\tan{\left(70 \right)}} \operatorname{asin}{\left(77 \right)}}$$
Más detalles con x→1 a la derecha
$$\lim_{x \to -\infty}\left(\frac{\log{\left(x + 1 \right)}}{\sqrt{\tan{\left(70 x \right)}} \operatorname{asin}{\left(77 \sqrt{x} \right)}}\right)$$
Más detalles con x→-oo
Más detalles con x→0 a la izquierda
$$\lim_{x \to 0^+}\left(\frac{\log{\left(x + 1 \right)}}{\sqrt{\tan{\left(70 x \right)}} \operatorname{asin}{\left(77 \sqrt{x} \right)}}\right) = \frac{\sqrt{70}}{5390}$$
$$\lim_{x \to \infty}\left(\frac{\log{\left(x + 1 \right)}}{\sqrt{\tan{\left(70 x \right)}} \operatorname{asin}{\left(77 \sqrt{x} \right)}}\right)$$
Más detalles con x→oo
$$\lim_{x \to 1^-}\left(\frac{\log{\left(x + 1 \right)}}{\sqrt{\tan{\left(70 x \right)}} \operatorname{asin}{\left(77 \sqrt{x} \right)}}\right) = \frac{\log{\left(2 \right)}}{\sqrt{\tan{\left(70 \right)}} \operatorname{asin}{\left(77 \right)}}$$
Más detalles con x→1 a la izquierda
$$\lim_{x \to 1^+}\left(\frac{\log{\left(x + 1 \right)}}{\sqrt{\tan{\left(70 x \right)}} \operatorname{asin}{\left(77 \sqrt{x} \right)}}\right) = \frac{\log{\left(2 \right)}}{\sqrt{\tan{\left(70 \right)}} \operatorname{asin}{\left(77 \right)}}$$
Más detalles con x→1 a la derecha
$$\lim_{x \to -\infty}\left(\frac{\log{\left(x + 1 \right)}}{\sqrt{\tan{\left(70 x \right)}} \operatorname{asin}{\left(77 \sqrt{x} \right)}}\right)$$
Más detalles con x→-oo
A la izquierda y a la derecha
[src]
/ log(1 + x) \
lim |----------------------------|
x->0+| / ___\ ___________|
\asin\77*\/ x /*\/ tan(70*x) /
$$\lim_{x \to 0^+}\left(\frac{\log{\left(x + 1 \right)}}{\sqrt{\tan{\left(70 x \right)}} \operatorname{asin}{\left(77 \sqrt{x} \right)}}\right)$$
____ \/ 70 ------ 5390
$$\frac{\sqrt{70}}{5390}$$
= (0.00166124896756775 + 0.0026671040065283j)
/ log(1 + x) \
lim |----------------------------|
x->0-| / ___\ ___________|
\asin\77*\/ x /*\/ tan(70*x) /
$$\lim_{x \to 0^-}\left(\frac{\log{\left(x + 1 \right)}}{\sqrt{\tan{\left(70 x \right)}} \operatorname{asin}{\left(77 \sqrt{x} \right)}}\right)$$
____ \/ 70 ------ 5390
$$\frac{\sqrt{70}}{5390}$$
= (0.0018849187901852 + 2.21039773206639e-7j)
= (0.0018849187901852 + 2.21039773206639e-7j)
Respuesta numérica
[src]
(0.00166124896756775 + 0.0026671040065283j)
(0.00166124896756775 + 0.0026671040065283j)