First slide

Introduction to limits

Question

$lim_{x \to \sqrt{3}} \frac{x^{2} - 3}{x^{2} + 3 \sqrt{3} x - 12}$ is equal to

Moderate

A

$\frac{1}{5}$
B

$\frac{2}{5}$
C

$\frac{\sqrt{3}}{5}$
D

$\frac{3}{5}$

Solution

We have,
$\begin{array}{l} lim_{x \to \sqrt{3}} \frac{x^{2} - 3}{x^{2} + 3 \sqrt{3} x - 12} \\ = lim_{x \to \sqrt{3}} \frac{(x - \sqrt{3}) (x + \sqrt{3})}{(x + 4 \sqrt{3}) (x - \sqrt{3})} = lim_{x \to \sqrt{3}} \frac{x + \sqrt{3}}{x + 4 \sqrt{3}} = \frac{2}{5} \end{array}$

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