Question

How do you use L'hospital's rule to find the limit `lim_(x->oo)x^3e^(-x^2)` ?

Answer 1

By rewriting

#lim_{x to infty}x^3e^{-x^2} =lim_{x to infty}{x^3}/{e^{x^2}}#

by l'Hopital's Rule,

`=lim_{x to infty}{3x^2}/{2xe^{x^2}}=lim_{x to infty}{3x}/{2e^{2x^2}}`

by another l'Hopital's Rule,

`=lim_{x to infty}{3}/{4xe^{x^2}}=3/infty=0`