Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
Advertisement Remove all ads

# Lim X → √ 3 X 4 − 9 X 2 + 4 √ 3 X − 15 - Mathematics

$\lim_{x \to \sqrt{3}} \frac{x^4 - 9}{x^2 + 4\sqrt{3}x - 15}$

Advertisement Remove all ads

#### Solution

$\lim_{x \to \sqrt{3}} \left[ \frac{x^4 - 9}{x^2 + 4\sqrt{3}x - 15} \right]$
$\text{ It is of the form } \frac{0}{0} .$
$\lim_{x \to \sqrt{3}} \left[ \frac{\left( x^2 \right)^2 - \left( 3 \right)^2}{x^2 + 5\sqrt{3}x - \sqrt{3}x - 15} \right]$
$= \lim_{x \to \sqrt{3}} \left[ \frac{\left( x^2 - 3 \right)\left( x^2 + 3 \right)}{x\left( x + 5\sqrt{3} \right) - \sqrt{3}\left( x + 5\sqrt{3} \right)} \right]$
$= \lim_{x \to \sqrt{3}} \left[ \frac{\left\{ x^2 - \left( \sqrt{3} \right)^2 \right\}\left( x^2 + 3 \right)}{\left( x - \sqrt{3} \right)\left( x + 5\sqrt{3} \right)} \right]$
$= \lim_{x \to \sqrt{3}} \left[ \frac{\left( x - \sqrt{3} \right)\left( x + \sqrt{3} \right)\left( x^2 + 3 \right)}{\left( x - \sqrt{3} \right)\left( x + 5\sqrt{3} \right)} \right]$
$= \frac{\left( \sqrt{3} + \sqrt{3} \right)\left( 3 + 3 \right)}{\sqrt{3} + 5\sqrt{3}}$
$= \frac{2\sqrt{3} \times 6}{6\sqrt{3}}$
$= 2$

Is there an error in this question or solution?
Advertisement Remove all ads

#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 29 Limits
Exercise 29.3 | Q 13 | Page 23
Advertisement Remove all ads

#### Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications

Forgot password?