# Lim of x^3 × e^(-x^2) as x approaches infinity?

##### 1 Answer

Jun 5, 2018

#### Explanation:

We want to solve

#L=lim_(x->oo)x^3*e^(-x^2)=lim_(x->oo)x^3/e^(x^2)#

Which is an indeterminate form

So we can apply **L'Hôpital's rule**

#color(blue)(lim_(x->c)f(x)/g(x)=lim_(x->c)(f'(x))/(g'(x))#

Thus

#L=lim_(x->oo)(3x^2)/(2xe^(x^2))=lim_(x->oo)(3x)/(2e^(x^2))#

Again an indeterminate form

#L=lim_(x->oo)(3)/(4xe^(x^2))=0#