Functions Question 233
Question: $ \underset{x\to 0}{\mathop{\lim }}\frac{ln,(\cos x)}{x^{2}} $ is equal to
[AMU 2000]
Options:
A) 0
B) 1
C) $ \frac{1}{2} $
D) $ -\frac{1}{2} $
Show Answer
Answer:
Correct Answer: D
Solution:
Applying L-Hospital?s rule, $ \underset{x\to 0}{\mathop{\lim }},\frac{\ln (\cos x)}{x^{2}} $ $ =\underset{x\to 0}{\mathop{\lim }},\frac{-\tan x}{2x} $ $ =\underset{x\to 0}{\mathop{\lim }},\frac{-{{\sec }^{2}}x}{2}=\frac{-1}{2} $ .
BETA
