Question

Evaluate ${lim}_{x\to \infty }\frac{1}{x^n},n>1.$

Answer 1

${lim}_{x\to \infty }\frac{1}{x^n}$

If $x\to \infty$, then $\frac{1}{x}\to 0$

Then for $n>1$

$x\to \infty$

$\Rightarrow x^n\to \infty \Rightarrow \frac{1}{x^n}\to 0$

Therefore, ${lim}_{x\to \infty }\frac{1}{x^n}=0$