Sr Examen
Otras calculadoras:
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- Límite de la función:
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Límite de (1+4/x)^(2*x)
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Límite de (1-7/x)^x
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Límite de (1-cos(x)*cos(2*x)*cos(3*x))/(1-cos(x))
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Límite de (x-x^3+5*x^2)/(-x^2+2*x^3+7*x)
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Expresiones idénticas
- exp(sqrt(uno +n)*(im(x)^ dos +re(x)^ dos)^(uno / cuatro)*cos(twoatan(im(x),re(x))/ dos))*exp(-sqrt(n)*(im(x)^ dos +re(x)^ dos)^(uno / cuatro)*cos(twoatan(im(x),re(x))/ dos))
- exponente de ( raíz cuadrada de (1 más n) multiplicar por (im(x) al cuadrado más re(x) al cuadrado ) en el grado (1 dividir por 4) multiplicar por coseno de (two arco tangente de gente de (im(x),re(x)) dividir por 2)) multiplicar por exponente de ( menos raíz cuadrada de (n) multiplicar por (im(x) al cuadrado más re(x) al cuadrado ) en el grado (1 dividir por 4) multiplicar por coseno de (two arco tangente de gente de (im(x),re(x)) dividir por 2))
- exponente de ( raíz cuadrada de (uno más n) multiplicar por (im(x) en el grado dos más re(x) en el grado dos) en el grado (uno dividir por cuatro) multiplicar por coseno de (two arco tangente de gente de (im(x),re(x)) dividir por dos)) multiplicar por exponente de ( menos raíz cuadrada de (n) multiplicar por (im(x) en el grado dos más re(x) en el grado dos) en el grado (uno dividir por cuatro) multiplicar por coseno de (two arco tangente de gente de (im(x),re(x)) dividir por dos))
- exp(√(1+n)*(im(x)^2+re(x)^2)^(1/4)*cos(twoatan(im(x),re(x))/2))*exp(-√(n)*(im(x)^2+re(x)^2)^(1/4)*cos(twoatan(im(x),re(x))/2))
- exp(sqrt(1+n)*(im(x)2+re(x)2)(1/4)*cos(twoatan(im(x),re(x))/2))*exp(-sqrt(n)*(im(x)2+re(x)2)(1/4)*cos(twoatan(im(x),re(x))/2))
- expsqrt1+n*imx2+rex21/4*costwoatanimx,rex/2*exp-sqrtn*imx2+rex21/4*costwoatanimx,rex/2
- exp(sqrt(1+n)*(im(x)²+re(x)²)^(1/4)*cos(twoatan(im(x),re(x))/2))*exp(-sqrt(n)*(im(x)²+re(x)²)^(1/4)*cos(twoatan(im(x),re(x))/2))
- exp(sqrt(1+n)*(im(x) en el grado 2+re(x) en el grado 2) en el grado (1/4)*cos(twoatan(im(x),re(x))/2))*exp(-sqrt(n)*(im(x) en el grado 2+re(x) en el grado 2) en el grado (1/4)*cos(twoatan(im(x),re(x))/2))
- exp(sqrt(1+n)(im(x)^2+re(x)^2)^(1/4)cos(twoatan(im(x),re(x))/2))exp(-sqrt(n)(im(x)^2+re(x)^2)^(1/4)cos(twoatan(im(x),re(x))/2))
- exp(sqrt(1+n)(im(x)2+re(x)2)(1/4)cos(twoatan(im(x),re(x))/2))exp(-sqrt(n)(im(x)2+re(x)2)(1/4)cos(twoatan(im(x),re(x))/2))
- expsqrt1+nimx2+rex21/4costwoatanimx,rex/2exp-sqrtnimx2+rex21/4costwoatanimx,rex/2
- expsqrt1+nimx^2+rex^2^1/4costwoatanimx,rex/2exp-sqrtnimx^2+rex^2^1/4costwoatanimx,rex/2
- exp(sqrt(1+n)*(im(x)^2+re(x)^2)^(1 dividir por 4)*cos(twoatan(im(x),re(x)) dividir por 2))*exp(-sqrt(n)*(im(x)^2+re(x)^2)^(1 dividir por 4)*cos(twoatan(im(x),re(x)) dividir por 2))
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Expresiones semejantes
- exp(sqrt(1-n)*(im(x)^2+re(x)^2)^(1/4)*cos(twoatan(im(x),re(x))/2))*exp(-sqrt(n)*(im(x)^2+re(x)^2)^(1/4)*cos(twoatan(im(x),re(x))/2))
- exp(sqrt(1+n)*(im(x)^2+re(x)^2)^(1/4)*cos(twoatan(im(x),re(x))/2))*exp(-sqrt(n)*(im(x)^2-re(x)^2)^(1/4)*cos(twoatan(im(x),re(x))/2))
- exp(sqrt(1+n)*(im(x)^2+re(x)^2)^(1/4)*cos(twoatan(im(x),re(x))/2))*exp(sqrt(n)*(im(x)^2+re(x)^2)^(1/4)*cos(twoatan(im(x),re(x))/2))
- exp(sqrt(1+n)*(im(x)^2-re(x)^2)^(1/4)*cos(twoatan(im(x),re(x))/2))*exp(-sqrt(n)*(im(x)^2+re(x)^2)^(1/4)*cos(twoatan(im(x),re(x))/2))
- exp(sqrt(1+n)*(im(x)^2+re(x)^2)^(1/4)*cos(twoarctan(im(x),re(x))/2))*exp(-sqrt(n)*(im(x)^2+re(x)^2)^(1/4)*cos(twoarctan(im(x),re(x))/2))
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Expresiones con funciones
- Exponente exp
- exp(x^2/(-1+x^2))
- exp(1/(3+x))
- exp(-1+x)/(1+x)
- exp(x)/(x^3+3*log(x))
- exp(tan(x))^(x^(-3))-exp(-x^2+2*x)+exp(sin(x))
- Raíz cuadrada sqrt
- sqrt((2+x)*(3+x))-x
- sqrt(-1-2*x+4*x^2)-sqrt(-8-3*x+4*x^2)
- sqrt(-6+3*x)*(-sqrt(-8+3*x)+2*sqrt(-1+x))
- sqrt(x)+(x^2-x)^(1/3)
- sqrt(-9+x^2)-sqrt(-3+x^2+5*x)
- Coseno cos
- cos(2*x)^(-1/(4*x^2))
- cos(pi*t/3)
- cos(x)/2-pi
- cos((-1+pi*x)/(2*x))
- cos(2*x)^2*sin(x)/sin(3*x)
- Exponente exp
- exp(x^2/(-1+x^2))
- exp(1/(3+x))
- exp(-1+x)/(1+x)
- exp(x)/(x^3+3*log(x))
- exp(tan(x))^(x^(-3))-exp(-x^2+2*x)+exp(sin(x))
- Raíz cuadrada sqrt
- sqrt((2+x)*(3+x))-x
- sqrt(-1-2*x+4*x^2)-sqrt(-8-3*x+4*x^2)
- sqrt(-6+3*x)*(-sqrt(-8+3*x)+2*sqrt(-1+x))
- sqrt(x)+(x^2-x)^(1/3)
- sqrt(-9+x^2)-sqrt(-3+x^2+5*x)
- Coseno cos
- cos(2*x)^(-1/(4*x^2))
- cos(pi*t/3)
- cos(x)/2-pi
- cos((-1+pi*x)/(2*x))
- cos(2*x)^2*sin(x)/sin(3*x)
Límite de la función/
exp(sqrt(1+n)*(im(x)^2+re(x)^2)^(1/4)*cos(twoatan(im(x),re(x))/2))*exp(-sqrt(n)*(im(x)^2+re(x)^2)^(1/4)*cos(twoatan(im(x),re(x))/2))
Límite de la función exp(sqrt(1+n)*(im(x)^2+re(x)^2)^(1/4)*cos(twoatan(im(x),re(x))/2))*exp(-sqrt(n)*(im(x)^2+re(x)^2)^(1/4)*cos(twoatan(im(x),re(x))/2))
Solución
Ha introducido
[src]
/ _________________ _________________ \
| _______ 4 / 2 2 /atan2(im(x), re(x))\ ___ 4 / 2 2 /atan2(im(x), re(x))\|
| \/ 1 + n *\/ im (x) + re (x) *cos|-------------------| -\/ n *\/ im (x) + re (x) *cos|-------------------||
| \ 2 / \ 2 /|
lim \e *e /
n->oo
$$\lim_{n \to \infty}\left(e^{- \sqrt{n} \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}} e^{\sqrt{n + 1} \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}\right)$$
Limit(exp((sqrt(1 + n)*(im(x)^2 + re(x)^2)^(1/4))*cos(atan2(im(x), re(x))/2))*exp(((-sqrt(n))*(im(x)^2 + re(x)^2)^(1/4))*cos(atan2(im(x), re(x))/2)), n, oo, dir='-')
Otros límites con n→0, -oo, +oo, 1
$$\lim_{n \to \infty}\left(e^{- \sqrt{n} \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}} e^{\sqrt{n + 1} \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}\right) = 1$$
$$\lim_{n \to 0^-}\left(e^{- \sqrt{n} \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}} e^{\sqrt{n + 1} \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}\right) = e^{\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}$$
Más detalles con n→0 a la izquierda
$$\lim_{n \to 0^+}\left(e^{- \sqrt{n} \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}} e^{\sqrt{n + 1} \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}\right) = e^{\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}$$
Más detalles con n→0 a la derecha
$$\lim_{n \to 1^-}\left(e^{- \sqrt{n} \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}} e^{\sqrt{n + 1} \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}\right) = e^{- \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}} e^{\sqrt{2} \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}$$
Más detalles con n→1 a la izquierda
$$\lim_{n \to 1^+}\left(e^{- \sqrt{n} \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}} e^{\sqrt{n + 1} \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}\right) = e^{- \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}} e^{\sqrt{2} \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}$$
Más detalles con n→1 a la derecha
$$\lim_{n \to -\infty}\left(e^{- \sqrt{n} \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}} e^{\sqrt{n + 1} \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}\right) = 1$$
Más detalles con n→-oo
$$\lim_{n \to 0^-}\left(e^{- \sqrt{n} \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}} e^{\sqrt{n + 1} \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}\right) = e^{\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}$$
Más detalles con n→0 a la izquierda
$$\lim_{n \to 0^+}\left(e^{- \sqrt{n} \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}} e^{\sqrt{n + 1} \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}\right) = e^{\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}$$
Más detalles con n→0 a la derecha
$$\lim_{n \to 1^-}\left(e^{- \sqrt{n} \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}} e^{\sqrt{n + 1} \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}\right) = e^{- \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}} e^{\sqrt{2} \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}$$
Más detalles con n→1 a la izquierda
$$\lim_{n \to 1^+}\left(e^{- \sqrt{n} \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}} e^{\sqrt{n + 1} \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}\right) = e^{- \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}} e^{\sqrt{2} \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}$$
Más detalles con n→1 a la derecha
$$\lim_{n \to -\infty}\left(e^{- \sqrt{n} \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}} e^{\sqrt{n + 1} \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}\right) = 1$$
Más detalles con n→-oo