Functions Question 369
Question: If $ f(x),=\frac{2-\sqrt{x+4}}{\sin 2x},(x\ne 0), $ is continuous function at $ x=0 $ , then $ f(0) $ equals
[MP PET 2002]
Options:
A) $ \frac{1}{4} $
B) $ -\frac{1}{4} $
C) $ \frac{1}{8} $
D) $ -\frac{1}{8} $
Show Answer
Answer:
Correct Answer: D
Solution:
If $ f(x) $ is continuous at $ x=0, $ then $ f(0),=,\underset{x\to 0}{\mathop{\lim }},f(x) $ $ =\underset{x\to 0}{\mathop{\lim }},\frac{2-\sqrt{x+4}}{\sin 2x} $ , $ ( \frac{0}{0},form ) $ Using L?Hospital?s rule, $ f(0)=\underset{x\to 0}{\mathop{\lim }},\frac{( -\frac{1}{2\sqrt{x+4}} )}{2\cos 2x}=-\frac{1}{8} $ .
BETA
