Functions Question 7
Question: $ \underset{x\to 0}{\mathop{\lim }}\frac{\log \cos x}{x}= $
Options:
A) 0
B) 1
C) $ \infty $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ \underset{x\to 0}{\mathop{\lim }}\frac{\log \cos x}{x}=\underset{x\to 0}{\mathop{\lim }}\frac{\log [ 1-2{{\sin }^{2}}\frac{x}{2} ]}{x} $ $ =\underset{x\to 0}{\mathop{\lim }}\frac{-[ 2{{\sin }^{2}}\frac{x}{2}+{{( \frac{2{{\sin }^{2}}\frac{x}{2}}{2} )}^{2}}+…… ]}{x}=0 $ Aliter : Apply L-Hospital?s rule, $ \underset{x\to 0}{\mathop{\lim }}\frac{\log \cos x}{x}=\underset{x\to 0}{\mathop{\lim }}\frac{-\tan x}{1}=0. $
BETA
