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

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Answer 1 · 2014-09-21T16:06:27

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,

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

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