Functions Question 143
Question: $ \underset{x\to 0}{\mathop{\lim }},\frac{\sqrt{\frac{1}{2}(1-\cos 2x)}}{x}= $
[IIT 1991; AIEEE 2002; RPET 2001, 02]
Options:
A) 1
B) ?1
C) 0
D) None of these
Show Answer
Answer:
Correct Answer: D
Solution:
$ \underset{x\to 0}{\mathop{\lim }}\frac{\sqrt{\tfrac{1}{2}(1-\cos 2x)}}{x}=\underset{x\to 0}{\mathop{\lim }}\frac{|\sin x|}{x} $ So, $ \underset{x\to 0+}{\mathop{\lim }}\frac{|,\sin x,|}{x}=1 $ and $ \underset{x\to 0-}{\mathop{\lim }}\frac{|,\sin x,|}{x}=-1 $ Hence limit does not exist.
BETA
