First slide

Introduction to limits

Question

The value of $lim_{x \to 2 a} \frac{\sqrt{x - 2 a} + \sqrt{x} - \sqrt{2 a}}{\sqrt{x^{2} - 4 a^{2}}}$ , is

Moderate

A

$\frac{1}{\sqrt{a}}$
B

$\frac{1}{2 \sqrt{a}}$
C

$\frac{\sqrt{a}}{2}$
D

$2 \sqrt{a}$

Solution

We have,
$\begin{array}{l} lim_{x \to 2 a} \frac{\sqrt{x - 2 a} + \sqrt{x} - \sqrt{2 a}}{\sqrt{x^{2} - 4 a^{2}}} \\ = lim_{x \to 2 a} \frac{\sqrt{x - 2 a} + \frac{x - 2 a}{\sqrt{x} + \sqrt{2 a}}}{\sqrt{(x - 2 a)} \sqrt{(x + 2 a)}} \\ = lim_{x \to 2 a} \frac{1 + \frac{\sqrt{x - 2 a}}{(\sqrt{x} + \sqrt{2 a})}}{(\sqrt{x + 2 a)}} = \frac{1}{\sqrt{4 a}} = \frac{1}{2 \sqrt{a}} \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App