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Límite de (-10-x+3*x^2)/(-10-x^2+7*x)
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Límite de (-1+sqrt(1+x))/x
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Límite de sin(2*x)/sin(3*x)
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Límite de sin(5*x)/(2*x)
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Expresiones idénticas
- -x/log(uno -x)^ tres +tan(x)
- menos x dividir por logaritmo de (1 menos x) al cubo más tangente de (x)
- menos x dividir por logaritmo de (uno menos x) en el grado tres más tangente de (x)
- -x/log(1-x)3+tan(x)
- -x/log1-x3+tanx
- -x/log(1-x)³+tan(x)
- -x/log(1-x) en el grado 3+tan(x)
- -x/log1-x^3+tanx
- -x dividir por log(1-x)^3+tan(x)
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Expresiones semejantes
- x/log(1-x)^3+tan(x)
- -x/log(1-x)^3-tan(x)
- -x/log(1+x)^3+tan(x)
-
Expresiones con funciones
- Logaritmo log
- log(1+x)/log(x)
- log(1+sin(x))/sin(4*x)
- log(tan(x))/cos(2*x)
- log(x)/(1-x^3)
- log(cos(2*x))/x^2
- Tangente tan
- tan(x)^x
- tan(2*x)/sin(4*x)
- tan(-2+x)/log(3-x)
- tan(6*x)/(2*x)
- tan(5*x)/(2*x)
Límite de la función -x/log(1-x)^3+tan(x)
Solución
Ha introducido
[src]
/ -x \
lim |----------- + tan(x)|
x->0+| 3 |
\log (1 - x) /
$$\lim_{x \to 0^+}\left(\frac{\left(-1\right) x}{\log{\left(1 - x \right)}^{3}} + \tan{\left(x \right)}\right)$$
Limit((-x)/log(1 - x)^3 + tan(x), x, 0)
Método de l'Hopital
Tenemos la indeterminación de tipo
tal que el límite para el numerador es
$$\lim_{x \to 0^+}\left(- x + \log{\left(1 - x \right)}^{3} \tan{\left(x \right)}\right) = 0$$
y el límite para el denominador es
$$\lim_{x \to 0^+} \log{\left(1 - x \right)}^{3} = 0$$
Vamos a probar las derivadas del numerador y denominador hasta eliminar la indeterminación.
$$\lim_{x \to 0^+}\left(\frac{\left(-1\right) x}{\log{\left(1 - x \right)}^{3}} + \tan{\left(x \right)}\right)$$
=
Introducimos una pequeña modificación de la función bajo el signo del límite
$$\lim_{x \to 0^+}\left(\frac{- x + \log{\left(1 - x \right)}^{3} \tan{\left(x \right)}}{\log{\left(1 - x \right)}^{3}}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{\frac{d}{d x} \left(- x + \log{\left(1 - x \right)}^{3} \tan{\left(x \right)}\right)}{\frac{d}{d x} \log{\left(1 - x \right)}^{3}}\right)$$
=
$$\lim_{x \to 0^+}\left(- \frac{\left(1 - x\right) \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(1 - x \right)}^{3} - 1 - \frac{3 \log{\left(1 - x \right)}^{2} \tan{\left(x \right)}}{1 - x}\right)}{3 \log{\left(1 - x \right)}^{2}}\right)$$
=
$$\lim_{x \to 0^+}\left(- \frac{\log{\left(1 - x \right)}^{3} \tan^{2}{\left(x \right)} + \log{\left(1 - x \right)}^{3} - 1 - \frac{3 \log{\left(1 - x \right)}^{2} \tan{\left(x \right)}}{1 - x}}{3 \log{\left(1 - x \right)}^{2}}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{\frac{d}{d x} \left(\log{\left(1 - x \right)}^{3} \tan^{2}{\left(x \right)} + \log{\left(1 - x \right)}^{3} - 1 - \frac{3 \log{\left(1 - x \right)}^{2} \tan{\left(x \right)}}{1 - x}\right)}{\frac{d}{d x} \left(- 3 \log{\left(1 - x \right)}^{2}\right)}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{\left(1 - x\right) \left(\left(2 \tan^{2}{\left(x \right)} + 2\right) \log{\left(1 - x \right)}^{3} \tan{\left(x \right)} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(1 - x \right)}^{2}}{1 - x} - \frac{3 \log{\left(1 - x \right)}^{2} \tan^{2}{\left(x \right)}}{1 - x} - \frac{3 \log{\left(1 - x \right)}^{2}}{1 - x} - \frac{3 \log{\left(1 - x \right)}^{2} \tan{\left(x \right)}}{\left(1 - x\right)^{2}} + \frac{6 \log{\left(1 - x \right)} \tan{\left(x \right)}}{\left(1 - x\right)^{2}}\right)}{6 \log{\left(1 - x \right)}}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{2 \log{\left(1 - x \right)}^{3} \tan^{3}{\left(x \right)} + 2 \log{\left(1 - x \right)}^{3} \tan{\left(x \right)} - \frac{3 \log{\left(1 - x \right)}^{2} \tan{\left(x \right)}}{x^{2} - 2 x + 1} + \frac{6 \log{\left(1 - x \right)} \tan{\left(x \right)}}{x^{2} - 2 x + 1} - \frac{6 \log{\left(1 - x \right)}^{2} \tan^{2}{\left(x \right)}}{1 - x} - \frac{6 \log{\left(1 - x \right)}^{2}}{1 - x}}{6 \log{\left(1 - x \right)}}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{\frac{d}{d x} \left(2 \log{\left(1 - x \right)}^{3} \tan^{3}{\left(x \right)} + 2 \log{\left(1 - x \right)}^{3} \tan{\left(x \right)} - \frac{3 \log{\left(1 - x \right)}^{2} \tan{\left(x \right)}}{x^{2} - 2 x + 1} + \frac{6 \log{\left(1 - x \right)} \tan{\left(x \right)}}{x^{2} - 2 x + 1} - \frac{6 \log{\left(1 - x \right)}^{2} \tan^{2}{\left(x \right)}}{1 - x} - \frac{6 \log{\left(1 - x \right)}^{2}}{1 - x}\right)}{\frac{d}{d x} 6 \log{\left(1 - x \right)}}\right)$$
=
$$\lim_{x \to 0^+}\left(\left(\frac{x}{6} - \frac{1}{6}\right) \left(- \frac{3 \left(2 - 2 x\right) \log{\left(1 - x \right)}^{2} \tan{\left(x \right)}}{\left(x^{2} - 2 x + 1\right)^{2}} + \frac{6 \left(2 - 2 x\right) \log{\left(1 - x \right)} \tan{\left(x \right)}}{\left(x^{2} - 2 x + 1\right)^{2}} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(1 - x \right)}^{3} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(1 - x \right)}^{2}}{x^{2} - 2 x + 1} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(1 - x \right)}}{x^{2} - 2 x + 1} + 2 \left(3 \tan^{2}{\left(x \right)} + 3\right) \log{\left(1 - x \right)}^{3} \tan^{2}{\left(x \right)} - \frac{6 \left(2 \tan^{2}{\left(x \right)} + 2\right) \log{\left(1 - x \right)}^{2} \tan{\left(x \right)}}{1 - x} - \frac{6 \log{\left(1 - x \right)}^{2} \tan^{3}{\left(x \right)}}{1 - x} - \frac{6 \log{\left(1 - x \right)}^{2} \tan{\left(x \right)}}{1 - x} + \frac{6 \log{\left(1 - x \right)} \tan{\left(x \right)}}{\left(1 - x\right) \left(x^{2} - 2 x + 1\right)} - \frac{6 \tan{\left(x \right)}}{\left(1 - x\right) \left(x^{2} - 2 x + 1\right)} - \frac{6 \log{\left(1 - x \right)}^{2} \tan^{2}{\left(x \right)}}{\left(1 - x\right)^{2}} - \frac{6 \log{\left(1 - x \right)}^{2}}{\left(1 - x\right)^{2}} + \frac{12 \log{\left(1 - x \right)} \tan^{2}{\left(x \right)}}{\left(1 - x\right)^{2}} + \frac{12 \log{\left(1 - x \right)}}{\left(1 - x\right)^{2}}\right)\right)$$
=
$$\lim_{x \to 0^+}\left(- \frac{x \log{\left(1 - x \right)}^{2} \tan{\left(x \right)}}{x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1} + \frac{2 x \log{\left(1 - x \right)} \tan{\left(x \right)}}{x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1} - \log{\left(1 - x \right)}^{3} \tan^{4}{\left(x \right)} - \frac{4 \log{\left(1 - x \right)}^{3} \tan^{2}{\left(x \right)}}{3} - \frac{\log{\left(1 - x \right)}^{3}}{3} + \frac{\log{\left(1 - x \right)}^{2} \tan{\left(x \right)}}{x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1} - \frac{2 \log{\left(1 - x \right)} \tan{\left(x \right)}}{x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1} - \frac{\log{\left(1 - x \right)} \tan{\left(x \right)}}{- x^{3} + 3 x^{2} - 3 x + 1} + \frac{\tan{\left(x \right)}}{- x^{3} + 3 x^{2} - 3 x + 1} + \frac{3 \log{\left(1 - x \right)}^{2} \tan^{2}{\left(x \right)}}{2 \left(x^{2} - 2 x + 1\right)} + \frac{3 \log{\left(1 - x \right)}^{2}}{2 \left(x^{2} - 2 x + 1\right)} - \frac{3 \log{\left(1 - x \right)} \tan^{2}{\left(x \right)}}{x^{2} - 2 x + 1} - \frac{3 \log{\left(1 - x \right)}}{x^{2} - 2 x + 1} + \frac{3 \log{\left(1 - x \right)}^{2} \tan^{3}{\left(x \right)}}{1 - x} + \frac{3 \log{\left(1 - x \right)}^{2} \tan{\left(x \right)}}{1 - x}\right)$$
=
$$\lim_{x \to 0^+}\left(- \frac{x \log{\left(1 - x \right)}^{2} \tan{\left(x \right)}}{x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1} + \frac{2 x \log{\left(1 - x \right)} \tan{\left(x \right)}}{x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1} - \log{\left(1 - x \right)}^{3} \tan^{4}{\left(x \right)} - \frac{4 \log{\left(1 - x \right)}^{3} \tan^{2}{\left(x \right)}}{3} - \frac{\log{\left(1 - x \right)}^{3}}{3} + \frac{\log{\left(1 - x \right)}^{2} \tan{\left(x \right)}}{x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1} - \frac{2 \log{\left(1 - x \right)} \tan{\left(x \right)}}{x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1} - \frac{\log{\left(1 - x \right)} \tan{\left(x \right)}}{- x^{3} + 3 x^{2} - 3 x + 1} + \frac{\tan{\left(x \right)}}{- x^{3} + 3 x^{2} - 3 x + 1} + \frac{3 \log{\left(1 - x \right)}^{2} \tan^{2}{\left(x \right)}}{2 \left(x^{2} - 2 x + 1\right)} + \frac{3 \log{\left(1 - x \right)}^{2}}{2 \left(x^{2} - 2 x + 1\right)} - \frac{3 \log{\left(1 - x \right)} \tan^{2}{\left(x \right)}}{x^{2} - 2 x + 1} - \frac{3 \log{\left(1 - x \right)}}{x^{2} - 2 x + 1} + \frac{3 \log{\left(1 - x \right)}^{2} \tan^{3}{\left(x \right)}}{1 - x} + \frac{3 \log{\left(1 - x \right)}^{2} \tan{\left(x \right)}}{1 - x}\right)$$
=
$$\infty$$
Como puedes ver, hemos aplicado el método de l'Hopital (utilizando la derivada del numerador y denominador) 3 vez (veces)
0/0,
tal que el límite para el numerador es
$$\lim_{x \to 0^+}\left(- x + \log{\left(1 - x \right)}^{3} \tan{\left(x \right)}\right) = 0$$
y el límite para el denominador es
$$\lim_{x \to 0^+} \log{\left(1 - x \right)}^{3} = 0$$
Vamos a probar las derivadas del numerador y denominador hasta eliminar la indeterminación.
$$\lim_{x \to 0^+}\left(\frac{\left(-1\right) x}{\log{\left(1 - x \right)}^{3}} + \tan{\left(x \right)}\right)$$
=
Introducimos una pequeña modificación de la función bajo el signo del límite
$$\lim_{x \to 0^+}\left(\frac{- x + \log{\left(1 - x \right)}^{3} \tan{\left(x \right)}}{\log{\left(1 - x \right)}^{3}}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{\frac{d}{d x} \left(- x + \log{\left(1 - x \right)}^{3} \tan{\left(x \right)}\right)}{\frac{d}{d x} \log{\left(1 - x \right)}^{3}}\right)$$
=
$$\lim_{x \to 0^+}\left(- \frac{\left(1 - x\right) \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(1 - x \right)}^{3} - 1 - \frac{3 \log{\left(1 - x \right)}^{2} \tan{\left(x \right)}}{1 - x}\right)}{3 \log{\left(1 - x \right)}^{2}}\right)$$
=
$$\lim_{x \to 0^+}\left(- \frac{\log{\left(1 - x \right)}^{3} \tan^{2}{\left(x \right)} + \log{\left(1 - x \right)}^{3} - 1 - \frac{3 \log{\left(1 - x \right)}^{2} \tan{\left(x \right)}}{1 - x}}{3 \log{\left(1 - x \right)}^{2}}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{\frac{d}{d x} \left(\log{\left(1 - x \right)}^{3} \tan^{2}{\left(x \right)} + \log{\left(1 - x \right)}^{3} - 1 - \frac{3 \log{\left(1 - x \right)}^{2} \tan{\left(x \right)}}{1 - x}\right)}{\frac{d}{d x} \left(- 3 \log{\left(1 - x \right)}^{2}\right)}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{\left(1 - x\right) \left(\left(2 \tan^{2}{\left(x \right)} + 2\right) \log{\left(1 - x \right)}^{3} \tan{\left(x \right)} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(1 - x \right)}^{2}}{1 - x} - \frac{3 \log{\left(1 - x \right)}^{2} \tan^{2}{\left(x \right)}}{1 - x} - \frac{3 \log{\left(1 - x \right)}^{2}}{1 - x} - \frac{3 \log{\left(1 - x \right)}^{2} \tan{\left(x \right)}}{\left(1 - x\right)^{2}} + \frac{6 \log{\left(1 - x \right)} \tan{\left(x \right)}}{\left(1 - x\right)^{2}}\right)}{6 \log{\left(1 - x \right)}}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{2 \log{\left(1 - x \right)}^{3} \tan^{3}{\left(x \right)} + 2 \log{\left(1 - x \right)}^{3} \tan{\left(x \right)} - \frac{3 \log{\left(1 - x \right)}^{2} \tan{\left(x \right)}}{x^{2} - 2 x + 1} + \frac{6 \log{\left(1 - x \right)} \tan{\left(x \right)}}{x^{2} - 2 x + 1} - \frac{6 \log{\left(1 - x \right)}^{2} \tan^{2}{\left(x \right)}}{1 - x} - \frac{6 \log{\left(1 - x \right)}^{2}}{1 - x}}{6 \log{\left(1 - x \right)}}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{\frac{d}{d x} \left(2 \log{\left(1 - x \right)}^{3} \tan^{3}{\left(x \right)} + 2 \log{\left(1 - x \right)}^{3} \tan{\left(x \right)} - \frac{3 \log{\left(1 - x \right)}^{2} \tan{\left(x \right)}}{x^{2} - 2 x + 1} + \frac{6 \log{\left(1 - x \right)} \tan{\left(x \right)}}{x^{2} - 2 x + 1} - \frac{6 \log{\left(1 - x \right)}^{2} \tan^{2}{\left(x \right)}}{1 - x} - \frac{6 \log{\left(1 - x \right)}^{2}}{1 - x}\right)}{\frac{d}{d x} 6 \log{\left(1 - x \right)}}\right)$$
=
$$\lim_{x \to 0^+}\left(\left(\frac{x}{6} - \frac{1}{6}\right) \left(- \frac{3 \left(2 - 2 x\right) \log{\left(1 - x \right)}^{2} \tan{\left(x \right)}}{\left(x^{2} - 2 x + 1\right)^{2}} + \frac{6 \left(2 - 2 x\right) \log{\left(1 - x \right)} \tan{\left(x \right)}}{\left(x^{2} - 2 x + 1\right)^{2}} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(1 - x \right)}^{3} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(1 - x \right)}^{2}}{x^{2} - 2 x + 1} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(1 - x \right)}}{x^{2} - 2 x + 1} + 2 \left(3 \tan^{2}{\left(x \right)} + 3\right) \log{\left(1 - x \right)}^{3} \tan^{2}{\left(x \right)} - \frac{6 \left(2 \tan^{2}{\left(x \right)} + 2\right) \log{\left(1 - x \right)}^{2} \tan{\left(x \right)}}{1 - x} - \frac{6 \log{\left(1 - x \right)}^{2} \tan^{3}{\left(x \right)}}{1 - x} - \frac{6 \log{\left(1 - x \right)}^{2} \tan{\left(x \right)}}{1 - x} + \frac{6 \log{\left(1 - x \right)} \tan{\left(x \right)}}{\left(1 - x\right) \left(x^{2} - 2 x + 1\right)} - \frac{6 \tan{\left(x \right)}}{\left(1 - x\right) \left(x^{2} - 2 x + 1\right)} - \frac{6 \log{\left(1 - x \right)}^{2} \tan^{2}{\left(x \right)}}{\left(1 - x\right)^{2}} - \frac{6 \log{\left(1 - x \right)}^{2}}{\left(1 - x\right)^{2}} + \frac{12 \log{\left(1 - x \right)} \tan^{2}{\left(x \right)}}{\left(1 - x\right)^{2}} + \frac{12 \log{\left(1 - x \right)}}{\left(1 - x\right)^{2}}\right)\right)$$
=
$$\lim_{x \to 0^+}\left(- \frac{x \log{\left(1 - x \right)}^{2} \tan{\left(x \right)}}{x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1} + \frac{2 x \log{\left(1 - x \right)} \tan{\left(x \right)}}{x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1} - \log{\left(1 - x \right)}^{3} \tan^{4}{\left(x \right)} - \frac{4 \log{\left(1 - x \right)}^{3} \tan^{2}{\left(x \right)}}{3} - \frac{\log{\left(1 - x \right)}^{3}}{3} + \frac{\log{\left(1 - x \right)}^{2} \tan{\left(x \right)}}{x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1} - \frac{2 \log{\left(1 - x \right)} \tan{\left(x \right)}}{x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1} - \frac{\log{\left(1 - x \right)} \tan{\left(x \right)}}{- x^{3} + 3 x^{2} - 3 x + 1} + \frac{\tan{\left(x \right)}}{- x^{3} + 3 x^{2} - 3 x + 1} + \frac{3 \log{\left(1 - x \right)}^{2} \tan^{2}{\left(x \right)}}{2 \left(x^{2} - 2 x + 1\right)} + \frac{3 \log{\left(1 - x \right)}^{2}}{2 \left(x^{2} - 2 x + 1\right)} - \frac{3 \log{\left(1 - x \right)} \tan^{2}{\left(x \right)}}{x^{2} - 2 x + 1} - \frac{3 \log{\left(1 - x \right)}}{x^{2} - 2 x + 1} + \frac{3 \log{\left(1 - x \right)}^{2} \tan^{3}{\left(x \right)}}{1 - x} + \frac{3 \log{\left(1 - x \right)}^{2} \tan{\left(x \right)}}{1 - x}\right)$$
=
$$\lim_{x \to 0^+}\left(- \frac{x \log{\left(1 - x \right)}^{2} \tan{\left(x \right)}}{x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1} + \frac{2 x \log{\left(1 - x \right)} \tan{\left(x \right)}}{x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1} - \log{\left(1 - x \right)}^{3} \tan^{4}{\left(x \right)} - \frac{4 \log{\left(1 - x \right)}^{3} \tan^{2}{\left(x \right)}}{3} - \frac{\log{\left(1 - x \right)}^{3}}{3} + \frac{\log{\left(1 - x \right)}^{2} \tan{\left(x \right)}}{x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1} - \frac{2 \log{\left(1 - x \right)} \tan{\left(x \right)}}{x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1} - \frac{\log{\left(1 - x \right)} \tan{\left(x \right)}}{- x^{3} + 3 x^{2} - 3 x + 1} + \frac{\tan{\left(x \right)}}{- x^{3} + 3 x^{2} - 3 x + 1} + \frac{3 \log{\left(1 - x \right)}^{2} \tan^{2}{\left(x \right)}}{2 \left(x^{2} - 2 x + 1\right)} + \frac{3 \log{\left(1 - x \right)}^{2}}{2 \left(x^{2} - 2 x + 1\right)} - \frac{3 \log{\left(1 - x \right)} \tan^{2}{\left(x \right)}}{x^{2} - 2 x + 1} - \frac{3 \log{\left(1 - x \right)}}{x^{2} - 2 x + 1} + \frac{3 \log{\left(1 - x \right)}^{2} \tan^{3}{\left(x \right)}}{1 - x} + \frac{3 \log{\left(1 - x \right)}^{2} \tan{\left(x \right)}}{1 - x}\right)$$
=
$$\infty$$
Como puedes ver, hemos aplicado el método de l'Hopital (utilizando la derivada del numerador y denominador) 3 vez (veces)
Gráfica
A la izquierda y a la derecha
[src]
/ -x \
lim |----------- + tan(x)|
x->0+| 3 |
\log (1 - x) /
$$\lim_{x \to 0^+}\left(\frac{\left(-1\right) x}{\log{\left(1 - x \right)}^{3}} + \tan{\left(x \right)}\right)$$
oo
$$\infty$$
= 22575.0066227967
/ -x \
lim |----------- + tan(x)|
x->0-| 3 |
\log (1 - x) /
$$\lim_{x \to 0^-}\left(\frac{\left(-1\right) x}{\log{\left(1 - x \right)}^{3}} + \tan{\left(x \right)}\right)$$
oo
$$\infty$$
= 23027.9933775688
= 23027.9933775688
Otros límites con x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{\left(-1\right) x}{\log{\left(1 - x \right)}^{3}} + \tan{\left(x \right)}\right) = \infty$$
Más detalles con x→0 a la izquierda
$$\lim_{x \to 0^+}\left(\frac{\left(-1\right) x}{\log{\left(1 - x \right)}^{3}} + \tan{\left(x \right)}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{\left(-1\right) x}{\log{\left(1 - x \right)}^{3}} + \tan{\left(x \right)}\right)$$
Más detalles con x→oo
$$\lim_{x \to 1^-}\left(\frac{\left(-1\right) x}{\log{\left(1 - x \right)}^{3}} + \tan{\left(x \right)}\right) = \tan{\left(1 \right)}$$
Más detalles con x→1 a la izquierda
$$\lim_{x \to 1^+}\left(\frac{\left(-1\right) x}{\log{\left(1 - x \right)}^{3}} + \tan{\left(x \right)}\right) = \tan{\left(1 \right)}$$
Más detalles con x→1 a la derecha
$$\lim_{x \to -\infty}\left(\frac{\left(-1\right) x}{\log{\left(1 - x \right)}^{3}} + \tan{\left(x \right)}\right)$$
Más detalles con x→-oo
Más detalles con x→0 a la izquierda
$$\lim_{x \to 0^+}\left(\frac{\left(-1\right) x}{\log{\left(1 - x \right)}^{3}} + \tan{\left(x \right)}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{\left(-1\right) x}{\log{\left(1 - x \right)}^{3}} + \tan{\left(x \right)}\right)$$
Más detalles con x→oo
$$\lim_{x \to 1^-}\left(\frac{\left(-1\right) x}{\log{\left(1 - x \right)}^{3}} + \tan{\left(x \right)}\right) = \tan{\left(1 \right)}$$
Más detalles con x→1 a la izquierda
$$\lim_{x \to 1^+}\left(\frac{\left(-1\right) x}{\log{\left(1 - x \right)}^{3}} + \tan{\left(x \right)}\right) = \tan{\left(1 \right)}$$
Más detalles con x→1 a la derecha
$$\lim_{x \to -\infty}\left(\frac{\left(-1\right) x}{\log{\left(1 - x \right)}^{3}} + \tan{\left(x \right)}\right)$$
Más detalles con x→-oo