Q. 13 - Calculus

Question

Consider the limit expression

$\underset{x\to \infty }{\lim }(\sqrt{x}-x)$

Calculate the limit.

Step-by-Step Solution

Answer

The limit  of the expression is $\infty$

Step 1. Given

The given expression is 

$\underset{x\to \infty }{\lim }(\sqrt{x}-x)$

Step 2. Calculation

$$\begin{gathered} \underset{x\to \infty }{\lim }(\sqrt{x}-x) \\ =\underset{x\to \infty }{\lim }\left(\sqrt{x}\right)-\underset{x\to \infty }{\lim }\left(x\right) \\ =\sqrt{\infty }-\infty \\ =\infty -\infty \\ =\infty \end{gathered}$$