_ x 4 3-5+x 1-5-x = - Vidyadip

MCQ

$\lim _{x \rightarrow 4} \frac{3-\sqrt{5+x}}{1-\sqrt{5-x}}=$

A
$0$
B
$\frac{1}{3}$
✓
$-\frac{1}{3}$
D
does not exist

✓

Answer

Correct option: C.

$-\frac{1}{3}$

(C)
Applying L-Hospital's rule, we get
$\lim _{x \rightarrow 4} \frac{3-\sqrt{5+x}}{1-\sqrt{5-x}}=\lim _{x \rightarrow 4} \frac{\frac{1}{2 \sqrt{5+x}}}{-\frac{1}{2 \sqrt{5-x}}}$
$=-\lim _{x \rightarrow 4} \frac{\sqrt{5-x}}{\sqrt{5+x}}=\frac{-1}{\sqrt{9}}=-\frac{1}{3}$

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