Question

Solve the limit $\underset{x\to \mathrm{\infty }}{lim}{x}^{-\frac{2}{3}}$.

Short answer

$0$

Step-by-step solution

Given Information

Consider the limits $\underset{x\to \mathrm{\infty }}{lim}{x}^{-\frac{2}{3}}$.

Evaluate the limit

Let, $L=\underset{x\to \mathrm{\infty }}{lim}{x}^{-\frac{2}{3}}$

$L=\underset{x\to \mathrm{\infty }}{lim}\frac{1}{x^{\frac{2}{3}}}$

$L=\underset{x\to \mathrm{\infty }}{lim}\frac{1}{\mathrm{\infty }}$

$L=0$