Answer
$0$
Work Step by Step
$\lim _{x\rightarrow \infty }\dfrac {x^{3}}{e^{x2}}=\dfrac {\dfrac {d}{dx}\left( x^{3}\right) }{\dfrac {d}{dx}\left( e^{x2}\right) }=\dfrac {3x^{2}}{2xe^{x2}}=\dfrac {3x}{2ex2}=\dfrac {\dfrac {d}{dx}\left( 3x\right) }{\dfrac {d}{dx}\left( 2e^{x2}\right) }=\dfrac {3}{4xe^{x2}}=\dfrac {3}{\infty }=0$
