Q. 52 - Calculus

Question

Calculate each limit in Exercises 35–80.  

$\underset{x\to \infty }{\lim }(x^{-\frac{1}{3}}-x^{-\frac{1}{2}})$

Step-by-Step Solution

Answer

The limit is 0.

Step 1. Given Information:

Given expression:

$\underset{x\to \infty }{\lim }(x^{-\frac{1}{3}}-x^{-\frac{1}{2}})$

We want to calculate the value of expression.

Step 2. Solution:

Since $-\frac{1}{3} and -\frac{1}{2}$are negative power, as $x\to \infty$ we have $x^{-\frac{1}{3}}\to 0 and x^{-\frac{1}{2}}\to 0$

Therefore the limit is $0-0=0$