Answer
$0$
Work Step by Step
$\lim _{x\rightarrow \infty }\dfrac {x^{4}-1}{x^{5}+2}=\lim _{x\rightarrow \infty }\dfrac {x^{4}\left( 1-\dfrac {7}{x^{4}}\right) }{x^{4}\left( x+\dfrac {2}{x^{4}}\right) }=\lim _{x\rightarrow \infty }\dfrac {\left( 1-\dfrac {7}{x^{4}}\right) }{x+\dfrac {2}{x^{4}}}=\lim _{x\rightarrow \infty }\dfrac {1-0}{x+0}=\lim _{x\rightarrow \infty }\dfrac {1}{x}=0$
