Functions Question 96
Question: $ \underset{x\to 0}{\mathop{\lim }},\frac{x{{.2}^{x}}-x}{1-\cos x}= $
[IIT 1980; BIT Ranchi 1983; RPET 2001]
Options:
A) 0
B) $ \log 4 $
C) $ \log 2 $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ \underset{x\to 0}{\mathop{\lim }}\frac{x.(2^{x}-1)}{1-\cos x}=\underset{x\to 0}{\mathop{\lim }},\frac{2^{x}-1}{x}.\frac{x^{2}}{1-\cos x} $ $ =\log 2,.\underset{x\to 0}{\mathop{\lim }},\frac{x^{2}}{2{{\sin }^{2}}\frac{x}{2}}=(\log 2),.,2=2\log 2=\log 4 $ .
BETA
