Answer
$\infty$
Work Step by Step
$\lim _{x\rightarrow \infty }\dfrac {e^x}{x^{4}}=\dfrac {\dfrac {d}{dx}\left( e^x\right) }{\dfrac {d}{dx}\left( x^{4}\right) }=\dfrac {e^x}{4x^{3}}=\dfrac {\dfrac {d}{dx}\left( e^x\right) }{\dfrac {d}{dx}\left( 4x^{3}\right) }=\dfrac {e^x}{12x^{2}}=\dfrac {\dfrac {d}{dx}\left( e^x\right) }{\dfrac {d}{dx}\left( 12x^{2}\right) }=\dfrac {e^x}{24x}=\dfrac {\dfrac {d}{dx}\left( e^x\right) }{\dfrac {d}{dx}\left( 24x\right) }=\dfrac {e^x}{24}=\infty $
