limx→3 x2−3x2+33x−12is equal to - Infinity Learn by Sri Chaitanya

A
$\frac{1}{5}$
B
$\frac{2}{5}$
C
$\frac{\sqrt{3}}{5}$
D
$\frac{3}{5}$

Solution:

We have,

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

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