What is the limit of x to infinity of x^2-3/e^x?

1 Answer
Jun 8, 2018

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

Explanation:

We want to evaluate the limit

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

Which is an indeterminate form #(oo)/(oo)#

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)(2x)/e^x#

An indeterminate form #(oo)/(oo)#, so apply LHR again

#L=lim_(x->oo)(2)/e^x=0#