Functions Question 273
Question: The value of $ \underset{x\to 7}{\mathop{\lim }},\frac{2-\sqrt{x-3}}{x^{2}-49} $ is
[MP PET 2003]
Options:
A) $ \frac{2}{9} $
B) $ -\frac{2}{49} $
C) $ \frac{1}{56} $
D) $ -\frac{1}{56} $
Show Answer
Answer:
Correct Answer: D
Solution:
Applying L-Hospital?s rule, $ \underset{x\to 7}{\mathop{\lim }},\frac{2-\sqrt{x-3}}{x^{2}-49} $ = $ \underset{x\to 7}{\mathop{\lim }},\frac{0-\frac{1}{2\sqrt{x-3}}}{2x} $ $ =\underset{x\to 7}{\mathop{\lim }},\frac{-1}{4x\sqrt{x-3}}=\frac{-1}{4.7\sqrt{7-3}}=\frac{-1}{56} $ .
BETA
