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- Límite de la función:
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Límite de 8*x/(-4+x)
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Límite de ((-7+2*x^2+21*x)/(9+2*x^2+18*x))^(1+2*x)
-
Límite de (-4-7*x+2*x^2)/(4-13*x+3*x^2)
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Límite de ((2+2*x^2)/(1+2*x^2))^(x^2)
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Expresiones idénticas
- sin(cinco *x)^ dos *(uno +x^ tres - seis *x)/((cuatro +x^ dos)*asin(x^ dos + tres *x)*tan(doce *x))
- seno de (5 multiplicar por x) al cuadrado multiplicar por (1 más x al cubo menos 6 multiplicar por x) dividir por ((4 más x al cuadrado ) multiplicar por ar coseno de eno de (x al cuadrado más 3 multiplicar por x) multiplicar por tangente de (12 multiplicar por x))
- seno de (cinco multiplicar por x) en el grado dos multiplicar por (uno más x en el grado tres menos seis multiplicar por x) dividir por ((cuatro más x en el grado dos) multiplicar por ar coseno de eno de (x en el grado dos más tres multiplicar por x) multiplicar por tangente de (doce multiplicar por x))
- sin(5*x)2*(1+x3-6*x)/((4+x2)*asin(x2+3*x)*tan(12*x))
- sin5*x2*1+x3-6*x/4+x2*asinx2+3*x*tan12*x
- sin(5*x)²*(1+x³-6*x)/((4+x²)*asin(x²+3*x)*tan(12*x))
- sin(5*x) en el grado 2*(1+x en el grado 3-6*x)/((4+x en el grado 2)*asin(x en el grado 2+3*x)*tan(12*x))
- sin(5x)^2(1+x^3-6x)/((4+x^2)asin(x^2+3x)tan(12x))
- sin(5x)2(1+x3-6x)/((4+x2)asin(x2+3x)tan(12x))
- sin5x21+x3-6x/4+x2asinx2+3xtan12x
- sin5x^21+x^3-6x/4+x^2asinx^2+3xtan12x
- sin(5*x)^2*(1+x^3-6*x) dividir por ((4+x^2)*asin(x^2+3*x)*tan(12*x))
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Expresiones semejantes
- sin(5*x)^2*(1+x^3-6*x)/((4-x^2)*asin(x^2+3*x)*tan(12*x))
- sin(5*x)^2*(1+x^3-6*x)/((4+x^2)*asin(x^2-3*x)*tan(12*x))
- sin(5*x)^2*(1-x^3-6*x)/((4+x^2)*asin(x^2+3*x)*tan(12*x))
- sin(5*x)^2*(1+x^3+6*x)/((4+x^2)*asin(x^2+3*x)*tan(12*x))
- sin(5*x)^2*(1+x^3-6*x)/((4+x^2)*arcsin(x^2+3*x)*tan(12*x))
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Expresiones con funciones
- Seno sin
- sin(x)^5/x^3
- sin(x/(x-i))
- sin(2*x)^3*tan(3*x)/x^2
- sin(10+x)^2/(-8+sqrt(-36+x^2))
- sin(4*a)/x
- Arcoseno arcsin
- asin(2*x)/tan(3*x)
- asin(4*x)^2/(x*(-1+sqrt(1+sin(5*x))))
- asin(-3+x)/(-1+(13-4*x)^(1/4))
- asin(-48+3*x^2)^2/sin(-4+x)^2
- asin(7*x)^2/(9*x^2)
- Tangente tan
- tan(7*x)^4/(-4+4^(1+sin(x^4)))
- tan((2+x)^2)/(2*(-1+e^(sqrt(-5+x^2+4*x))))
- tan(2*x)^(-x+pi/4)
- tan(x)^5*log(x)
- tan(3*x)^3/tan(2*x)^3
Límite de la función sin(5*x)^2*(1+x^3-6*x)/((4+x^2)*asin(x^2+3*x)*tan(12*x))
Solución
Ha introducido
[src]
/ 2 / 3 \ \
| sin (5*x)*\1 + x - 6*x/ |
lim |---------------------------------|
x->0+|/ 2\ / 2 \ |
\\4 + x /*asin\x + 3*x/*tan(12*x)/
$$\lim_{x \to 0^+}\left(\frac{\left(- 6 x + \left(x^{3} + 1\right)\right) \sin^{2}{\left(5 x \right)}}{\left(x^{2} + 4\right) \operatorname{asin}{\left(x^{2} + 3 x \right)} \tan{\left(12 x \right)}}\right)$$
Limit((sin(5*x)^2*(1 + x^3 - 6*x))/((((4 + x^2)*asin(x^2 + 3*x))*tan(12*x))), x, 0)
Método de l'Hopital
Tenemos la indeterminación de tipo
tal que el límite para el numerador es
$$\lim_{x \to 0^+}\left(\frac{\left(x^{3} - 6 x + 1\right) \sin^{2}{\left(5 x \right)}}{\left(x^{2} + 4\right) \tan{\left(12 x \right)}}\right) = 0$$
y el límite para el denominador es
$$\lim_{x \to 0^+} \operatorname{asin}{\left(x \left(x + 3\right) \right)} = 0$$
Vamos a probar las derivadas del numerador y denominador hasta eliminar la indeterminación.
$$\lim_{x \to 0^+}\left(\frac{\left(- 6 x + \left(x^{3} + 1\right)\right) \sin^{2}{\left(5 x \right)}}{\left(x^{2} + 4\right) \operatorname{asin}{\left(x^{2} + 3 x \right)} \tan{\left(12 x \right)}}\right)$$
=
Introducimos una pequeña modificación de la función bajo el signo del límite
$$\lim_{x \to 0^+}\left(\frac{\left(x^{3} - 6 x + 1\right) \sin^{2}{\left(5 x \right)}}{\left(x^{2} + 4\right) \tan{\left(12 x \right)} \operatorname{asin}{\left(x \left(x + 3\right) \right)}}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{\frac{d}{d x} \frac{\left(x^{3} - 6 x + 1\right) \sin^{2}{\left(5 x \right)}}{\left(x^{2} + 4\right) \tan{\left(12 x \right)}}}{\frac{d}{d x} \operatorname{asin}{\left(x \left(x + 3\right) \right)}}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{\sqrt{- x^{2} \left(x + 3\right)^{2} + 1} \left(- \frac{2 x \left(x^{3} - 6 x + 1\right) \sin^{2}{\left(5 x \right)}}{\left(x^{2} + 4\right)^{2} \tan{\left(12 x \right)}} + \frac{\left(3 x^{2} - 6\right) \sin^{2}{\left(5 x \right)}}{\left(x^{2} + 4\right) \tan{\left(12 x \right)}} + \frac{\left(- 12 \tan^{2}{\left(12 x \right)} - 12\right) \left(x^{3} - 6 x + 1\right) \sin^{2}{\left(5 x \right)}}{\left(x^{2} + 4\right) \tan^{2}{\left(12 x \right)}} + \frac{10 \left(x^{3} - 6 x + 1\right) \sin{\left(5 x \right)} \cos{\left(5 x \right)}}{\left(x^{2} + 4\right) \tan{\left(12 x \right)}}\right)}{2 x + 3}\right)$$
=
$$\lim_{x \to 0^+}\left(- \frac{2 x^{4} \sin^{2}{\left(5 x \right)}}{3 x^{4} \tan{\left(12 x \right)} + 24 x^{2} \tan{\left(12 x \right)} + 48 \tan{\left(12 x \right)}} - \frac{12 x^{3} \sin^{2}{\left(5 x \right)} \tan^{2}{\left(12 x \right)}}{3 x^{2} \tan^{2}{\left(12 x \right)} + 12 \tan^{2}{\left(12 x \right)}} - \frac{12 x^{3} \sin^{2}{\left(5 x \right)}}{3 x^{2} \tan^{2}{\left(12 x \right)} + 12 \tan^{2}{\left(12 x \right)}} + \frac{10 x^{3} \sin{\left(5 x \right)} \cos{\left(5 x \right)}}{3 x^{2} \tan{\left(12 x \right)} + 12 \tan{\left(12 x \right)}} + \frac{12 x^{2} \sin^{2}{\left(5 x \right)}}{3 x^{4} \tan{\left(12 x \right)} + 24 x^{2} \tan{\left(12 x \right)} + 48 \tan{\left(12 x \right)}} + \frac{3 x^{2} \sin^{2}{\left(5 x \right)}}{3 x^{2} \tan{\left(12 x \right)} + 12 \tan{\left(12 x \right)}} - \frac{2 x \sin^{2}{\left(5 x \right)}}{3 x^{4} \tan{\left(12 x \right)} + 24 x^{2} \tan{\left(12 x \right)} + 48 \tan{\left(12 x \right)}} + \frac{72 x \sin^{2}{\left(5 x \right)} \tan^{2}{\left(12 x \right)}}{3 x^{2} \tan^{2}{\left(12 x \right)} + 12 \tan^{2}{\left(12 x \right)}} + \frac{72 x \sin^{2}{\left(5 x \right)}}{3 x^{2} \tan^{2}{\left(12 x \right)} + 12 \tan^{2}{\left(12 x \right)}} - \frac{60 x \sin{\left(5 x \right)} \cos{\left(5 x \right)}}{3 x^{2} \tan{\left(12 x \right)} + 12 \tan{\left(12 x \right)}} - \frac{12 \sin^{2}{\left(5 x \right)} \tan^{2}{\left(12 x \right)}}{3 x^{2} \tan^{2}{\left(12 x \right)} + 12 \tan^{2}{\left(12 x \right)}} - \frac{12 \sin^{2}{\left(5 x \right)}}{3 x^{2} \tan^{2}{\left(12 x \right)} + 12 \tan^{2}{\left(12 x \right)}} - \frac{6 \sin^{2}{\left(5 x \right)}}{3 x^{2} \tan{\left(12 x \right)} + 12 \tan{\left(12 x \right)}} + \frac{10 \sin{\left(5 x \right)} \cos{\left(5 x \right)}}{3 x^{2} \tan{\left(12 x \right)} + 12 \tan{\left(12 x \right)}}\right)$$
=
$$\lim_{x \to 0^+}\left(- \frac{2 x^{4} \sin^{2}{\left(5 x \right)}}{3 x^{4} \tan{\left(12 x \right)} + 24 x^{2} \tan{\left(12 x \right)} + 48 \tan{\left(12 x \right)}} - \frac{12 x^{3} \sin^{2}{\left(5 x \right)} \tan^{2}{\left(12 x \right)}}{3 x^{2} \tan^{2}{\left(12 x \right)} + 12 \tan^{2}{\left(12 x \right)}} - \frac{12 x^{3} \sin^{2}{\left(5 x \right)}}{3 x^{2} \tan^{2}{\left(12 x \right)} + 12 \tan^{2}{\left(12 x \right)}} + \frac{10 x^{3} \sin{\left(5 x \right)} \cos{\left(5 x \right)}}{3 x^{2} \tan{\left(12 x \right)} + 12 \tan{\left(12 x \right)}} + \frac{12 x^{2} \sin^{2}{\left(5 x \right)}}{3 x^{4} \tan{\left(12 x \right)} + 24 x^{2} \tan{\left(12 x \right)} + 48 \tan{\left(12 x \right)}} + \frac{3 x^{2} \sin^{2}{\left(5 x \right)}}{3 x^{2} \tan{\left(12 x \right)} + 12 \tan{\left(12 x \right)}} - \frac{2 x \sin^{2}{\left(5 x \right)}}{3 x^{4} \tan{\left(12 x \right)} + 24 x^{2} \tan{\left(12 x \right)} + 48 \tan{\left(12 x \right)}} + \frac{72 x \sin^{2}{\left(5 x \right)} \tan^{2}{\left(12 x \right)}}{3 x^{2} \tan^{2}{\left(12 x \right)} + 12 \tan^{2}{\left(12 x \right)}} + \frac{72 x \sin^{2}{\left(5 x \right)}}{3 x^{2} \tan^{2}{\left(12 x \right)} + 12 \tan^{2}{\left(12 x \right)}} - \frac{60 x \sin{\left(5 x \right)} \cos{\left(5 x \right)}}{3 x^{2} \tan{\left(12 x \right)} + 12 \tan{\left(12 x \right)}} - \frac{12 \sin^{2}{\left(5 x \right)} \tan^{2}{\left(12 x \right)}}{3 x^{2} \tan^{2}{\left(12 x \right)} + 12 \tan^{2}{\left(12 x \right)}} - \frac{12 \sin^{2}{\left(5 x \right)}}{3 x^{2} \tan^{2}{\left(12 x \right)} + 12 \tan^{2}{\left(12 x \right)}} - \frac{6 \sin^{2}{\left(5 x \right)}}{3 x^{2} \tan{\left(12 x \right)} + 12 \tan{\left(12 x \right)}} + \frac{10 \sin{\left(5 x \right)} \cos{\left(5 x \right)}}{3 x^{2} \tan{\left(12 x \right)} + 12 \tan{\left(12 x \right)}}\right)$$
=
$$\frac{25}{144}$$
Como puedes ver, hemos aplicado el método de l'Hopital (utilizando la derivada del numerador y denominador) 1 vez (veces)
0/0,
tal que el límite para el numerador es
$$\lim_{x \to 0^+}\left(\frac{\left(x^{3} - 6 x + 1\right) \sin^{2}{\left(5 x \right)}}{\left(x^{2} + 4\right) \tan{\left(12 x \right)}}\right) = 0$$
y el límite para el denominador es
$$\lim_{x \to 0^+} \operatorname{asin}{\left(x \left(x + 3\right) \right)} = 0$$
Vamos a probar las derivadas del numerador y denominador hasta eliminar la indeterminación.
$$\lim_{x \to 0^+}\left(\frac{\left(- 6 x + \left(x^{3} + 1\right)\right) \sin^{2}{\left(5 x \right)}}{\left(x^{2} + 4\right) \operatorname{asin}{\left(x^{2} + 3 x \right)} \tan{\left(12 x \right)}}\right)$$
=
Introducimos una pequeña modificación de la función bajo el signo del límite
$$\lim_{x \to 0^+}\left(\frac{\left(x^{3} - 6 x + 1\right) \sin^{2}{\left(5 x \right)}}{\left(x^{2} + 4\right) \tan{\left(12 x \right)} \operatorname{asin}{\left(x \left(x + 3\right) \right)}}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{\frac{d}{d x} \frac{\left(x^{3} - 6 x + 1\right) \sin^{2}{\left(5 x \right)}}{\left(x^{2} + 4\right) \tan{\left(12 x \right)}}}{\frac{d}{d x} \operatorname{asin}{\left(x \left(x + 3\right) \right)}}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{\sqrt{- x^{2} \left(x + 3\right)^{2} + 1} \left(- \frac{2 x \left(x^{3} - 6 x + 1\right) \sin^{2}{\left(5 x \right)}}{\left(x^{2} + 4\right)^{2} \tan{\left(12 x \right)}} + \frac{\left(3 x^{2} - 6\right) \sin^{2}{\left(5 x \right)}}{\left(x^{2} + 4\right) \tan{\left(12 x \right)}} + \frac{\left(- 12 \tan^{2}{\left(12 x \right)} - 12\right) \left(x^{3} - 6 x + 1\right) \sin^{2}{\left(5 x \right)}}{\left(x^{2} + 4\right) \tan^{2}{\left(12 x \right)}} + \frac{10 \left(x^{3} - 6 x + 1\right) \sin{\left(5 x \right)} \cos{\left(5 x \right)}}{\left(x^{2} + 4\right) \tan{\left(12 x \right)}}\right)}{2 x + 3}\right)$$
=
$$\lim_{x \to 0^+}\left(- \frac{2 x^{4} \sin^{2}{\left(5 x \right)}}{3 x^{4} \tan{\left(12 x \right)} + 24 x^{2} \tan{\left(12 x \right)} + 48 \tan{\left(12 x \right)}} - \frac{12 x^{3} \sin^{2}{\left(5 x \right)} \tan^{2}{\left(12 x \right)}}{3 x^{2} \tan^{2}{\left(12 x \right)} + 12 \tan^{2}{\left(12 x \right)}} - \frac{12 x^{3} \sin^{2}{\left(5 x \right)}}{3 x^{2} \tan^{2}{\left(12 x \right)} + 12 \tan^{2}{\left(12 x \right)}} + \frac{10 x^{3} \sin{\left(5 x \right)} \cos{\left(5 x \right)}}{3 x^{2} \tan{\left(12 x \right)} + 12 \tan{\left(12 x \right)}} + \frac{12 x^{2} \sin^{2}{\left(5 x \right)}}{3 x^{4} \tan{\left(12 x \right)} + 24 x^{2} \tan{\left(12 x \right)} + 48 \tan{\left(12 x \right)}} + \frac{3 x^{2} \sin^{2}{\left(5 x \right)}}{3 x^{2} \tan{\left(12 x \right)} + 12 \tan{\left(12 x \right)}} - \frac{2 x \sin^{2}{\left(5 x \right)}}{3 x^{4} \tan{\left(12 x \right)} + 24 x^{2} \tan{\left(12 x \right)} + 48 \tan{\left(12 x \right)}} + \frac{72 x \sin^{2}{\left(5 x \right)} \tan^{2}{\left(12 x \right)}}{3 x^{2} \tan^{2}{\left(12 x \right)} + 12 \tan^{2}{\left(12 x \right)}} + \frac{72 x \sin^{2}{\left(5 x \right)}}{3 x^{2} \tan^{2}{\left(12 x \right)} + 12 \tan^{2}{\left(12 x \right)}} - \frac{60 x \sin{\left(5 x \right)} \cos{\left(5 x \right)}}{3 x^{2} \tan{\left(12 x \right)} + 12 \tan{\left(12 x \right)}} - \frac{12 \sin^{2}{\left(5 x \right)} \tan^{2}{\left(12 x \right)}}{3 x^{2} \tan^{2}{\left(12 x \right)} + 12 \tan^{2}{\left(12 x \right)}} - \frac{12 \sin^{2}{\left(5 x \right)}}{3 x^{2} \tan^{2}{\left(12 x \right)} + 12 \tan^{2}{\left(12 x \right)}} - \frac{6 \sin^{2}{\left(5 x \right)}}{3 x^{2} \tan{\left(12 x \right)} + 12 \tan{\left(12 x \right)}} + \frac{10 \sin{\left(5 x \right)} \cos{\left(5 x \right)}}{3 x^{2} \tan{\left(12 x \right)} + 12 \tan{\left(12 x \right)}}\right)$$
=
$$\lim_{x \to 0^+}\left(- \frac{2 x^{4} \sin^{2}{\left(5 x \right)}}{3 x^{4} \tan{\left(12 x \right)} + 24 x^{2} \tan{\left(12 x \right)} + 48 \tan{\left(12 x \right)}} - \frac{12 x^{3} \sin^{2}{\left(5 x \right)} \tan^{2}{\left(12 x \right)}}{3 x^{2} \tan^{2}{\left(12 x \right)} + 12 \tan^{2}{\left(12 x \right)}} - \frac{12 x^{3} \sin^{2}{\left(5 x \right)}}{3 x^{2} \tan^{2}{\left(12 x \right)} + 12 \tan^{2}{\left(12 x \right)}} + \frac{10 x^{3} \sin{\left(5 x \right)} \cos{\left(5 x \right)}}{3 x^{2} \tan{\left(12 x \right)} + 12 \tan{\left(12 x \right)}} + \frac{12 x^{2} \sin^{2}{\left(5 x \right)}}{3 x^{4} \tan{\left(12 x \right)} + 24 x^{2} \tan{\left(12 x \right)} + 48 \tan{\left(12 x \right)}} + \frac{3 x^{2} \sin^{2}{\left(5 x \right)}}{3 x^{2} \tan{\left(12 x \right)} + 12 \tan{\left(12 x \right)}} - \frac{2 x \sin^{2}{\left(5 x \right)}}{3 x^{4} \tan{\left(12 x \right)} + 24 x^{2} \tan{\left(12 x \right)} + 48 \tan{\left(12 x \right)}} + \frac{72 x \sin^{2}{\left(5 x \right)} \tan^{2}{\left(12 x \right)}}{3 x^{2} \tan^{2}{\left(12 x \right)} + 12 \tan^{2}{\left(12 x \right)}} + \frac{72 x \sin^{2}{\left(5 x \right)}}{3 x^{2} \tan^{2}{\left(12 x \right)} + 12 \tan^{2}{\left(12 x \right)}} - \frac{60 x \sin{\left(5 x \right)} \cos{\left(5 x \right)}}{3 x^{2} \tan{\left(12 x \right)} + 12 \tan{\left(12 x \right)}} - \frac{12 \sin^{2}{\left(5 x \right)} \tan^{2}{\left(12 x \right)}}{3 x^{2} \tan^{2}{\left(12 x \right)} + 12 \tan^{2}{\left(12 x \right)}} - \frac{12 \sin^{2}{\left(5 x \right)}}{3 x^{2} \tan^{2}{\left(12 x \right)} + 12 \tan^{2}{\left(12 x \right)}} - \frac{6 \sin^{2}{\left(5 x \right)}}{3 x^{2} \tan{\left(12 x \right)} + 12 \tan{\left(12 x \right)}} + \frac{10 \sin{\left(5 x \right)} \cos{\left(5 x \right)}}{3 x^{2} \tan{\left(12 x \right)} + 12 \tan{\left(12 x \right)}}\right)$$
=
$$\frac{25}{144}$$
Como puedes ver, hemos aplicado el método de l'Hopital (utilizando la derivada del numerador y denominador) 1 vez (veces)
Gráfica
A la izquierda y a la derecha
[src]
/ 2 / 3 \ \
| sin (5*x)*\1 + x - 6*x/ |
lim |---------------------------------|
x->0+|/ 2\ / 2 \ |
\\4 + x /*asin\x + 3*x/*tan(12*x)/
$$\lim_{x \to 0^+}\left(\frac{\left(- 6 x + \left(x^{3} + 1\right)\right) \sin^{2}{\left(5 x \right)}}{\left(x^{2} + 4\right) \operatorname{asin}{\left(x^{2} + 3 x \right)} \tan{\left(12 x \right)}}\right)$$
25 --- 144
$$\frac{25}{144}$$
= 0.173611111111111
/ 2 / 3 \ \
| sin (5*x)*\1 + x - 6*x/ |
lim |---------------------------------|
x->0-|/ 2\ / 2 \ |
\\4 + x /*asin\x + 3*x/*tan(12*x)/
$$\lim_{x \to 0^-}\left(\frac{\left(- 6 x + \left(x^{3} + 1\right)\right) \sin^{2}{\left(5 x \right)}}{\left(x^{2} + 4\right) \operatorname{asin}{\left(x^{2} + 3 x \right)} \tan{\left(12 x \right)}}\right)$$
25 --- 144
$$\frac{25}{144}$$
= 0.173611111111111
= 0.173611111111111
Otros límites con x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{\left(- 6 x + \left(x^{3} + 1\right)\right) \sin^{2}{\left(5 x \right)}}{\left(x^{2} + 4\right) \operatorname{asin}{\left(x^{2} + 3 x \right)} \tan{\left(12 x \right)}}\right) = \frac{25}{144}$$
Más detalles con x→0 a la izquierda
$$\lim_{x \to 0^+}\left(\frac{\left(- 6 x + \left(x^{3} + 1\right)\right) \sin^{2}{\left(5 x \right)}}{\left(x^{2} + 4\right) \operatorname{asin}{\left(x^{2} + 3 x \right)} \tan{\left(12 x \right)}}\right) = \frac{25}{144}$$
$$\lim_{x \to \infty}\left(\frac{\left(- 6 x + \left(x^{3} + 1\right)\right) \sin^{2}{\left(5 x \right)}}{\left(x^{2} + 4\right) \operatorname{asin}{\left(x^{2} + 3 x \right)} \tan{\left(12 x \right)}}\right)$$
Más detalles con x→oo
$$\lim_{x \to 1^-}\left(\frac{\left(- 6 x + \left(x^{3} + 1\right)\right) \sin^{2}{\left(5 x \right)}}{\left(x^{2} + 4\right) \operatorname{asin}{\left(x^{2} + 3 x \right)} \tan{\left(12 x \right)}}\right) = - \frac{4 \sin^{2}{\left(5 \right)}}{5 \tan{\left(12 \right)} \operatorname{asin}{\left(4 \right)}}$$
Más detalles con x→1 a la izquierda
$$\lim_{x \to 1^+}\left(\frac{\left(- 6 x + \left(x^{3} + 1\right)\right) \sin^{2}{\left(5 x \right)}}{\left(x^{2} + 4\right) \operatorname{asin}{\left(x^{2} + 3 x \right)} \tan{\left(12 x \right)}}\right) = - \frac{4 \sin^{2}{\left(5 \right)}}{5 \tan{\left(12 \right)} \operatorname{asin}{\left(4 \right)}}$$
Más detalles con x→1 a la derecha
$$\lim_{x \to -\infty}\left(\frac{\left(- 6 x + \left(x^{3} + 1\right)\right) \sin^{2}{\left(5 x \right)}}{\left(x^{2} + 4\right) \operatorname{asin}{\left(x^{2} + 3 x \right)} \tan{\left(12 x \right)}}\right)$$
Más detalles con x→-oo
Más detalles con x→0 a la izquierda
$$\lim_{x \to 0^+}\left(\frac{\left(- 6 x + \left(x^{3} + 1\right)\right) \sin^{2}{\left(5 x \right)}}{\left(x^{2} + 4\right) \operatorname{asin}{\left(x^{2} + 3 x \right)} \tan{\left(12 x \right)}}\right) = \frac{25}{144}$$
$$\lim_{x \to \infty}\left(\frac{\left(- 6 x + \left(x^{3} + 1\right)\right) \sin^{2}{\left(5 x \right)}}{\left(x^{2} + 4\right) \operatorname{asin}{\left(x^{2} + 3 x \right)} \tan{\left(12 x \right)}}\right)$$
Más detalles con x→oo
$$\lim_{x \to 1^-}\left(\frac{\left(- 6 x + \left(x^{3} + 1\right)\right) \sin^{2}{\left(5 x \right)}}{\left(x^{2} + 4\right) \operatorname{asin}{\left(x^{2} + 3 x \right)} \tan{\left(12 x \right)}}\right) = - \frac{4 \sin^{2}{\left(5 \right)}}{5 \tan{\left(12 \right)} \operatorname{asin}{\left(4 \right)}}$$
Más detalles con x→1 a la izquierda
$$\lim_{x \to 1^+}\left(\frac{\left(- 6 x + \left(x^{3} + 1\right)\right) \sin^{2}{\left(5 x \right)}}{\left(x^{2} + 4\right) \operatorname{asin}{\left(x^{2} + 3 x \right)} \tan{\left(12 x \right)}}\right) = - \frac{4 \sin^{2}{\left(5 \right)}}{5 \tan{\left(12 \right)} \operatorname{asin}{\left(4 \right)}}$$
Más detalles con x→1 a la derecha
$$\lim_{x \to -\infty}\left(\frac{\left(- 6 x + \left(x^{3} + 1\right)\right) \sin^{2}{\left(5 x \right)}}{\left(x^{2} + 4\right) \operatorname{asin}{\left(x^{2} + 3 x \right)} \tan{\left(12 x \right)}}\right)$$
Más detalles con x→-oo