Q. 21 - Calculus

Question

Consider the limit expression

$\underset{x\to \infty }{\lim }\frac{\sqrt{x}}{1-\sqrt{x}}$

Calculate the limit.

Step-by-Step Solution

Answer

The limit  of the expression is $\infty .$

Step 1. Given

The given expression is $\underset{x\to \infty }{\lim }\frac{\sqrt{x}}{1-\sqrt{x}}$.

Step 2. Calculation

The evaluated expression is 

$$\begin{gathered} \underset{x\to \infty }{\lim }\frac{\sqrt{x}}{1-\sqrt{x}} \\ =\frac{{\lim }_{x\to \infty }\sqrt{x}}{{\lim }_{x\to \infty }(1-\sqrt{x})} \\ =\frac{{\lim }_{x\to \infty }\sqrt{x}}{{\lim }_{x\to \infty }1-{\lim }_{x\to \infty }\sqrt{x}} \\ =\frac{\sqrt{\infty }}{1-\sqrt{\infty }} \\ =\frac{\infty }{\infty } \\ =\infty \end{gathered}$$