Functions Question 249
Question: $ \underset{x\to 0}{\mathop{\lim }},\frac{\sin (\pi {{\cos }^{2}}x)}{x^{2}}= $
[IIT Screening 2001;UPSEAT 2001; MP PET 2002]
Options:
A) $ (-1,1) $
B) $ \pi $
C) $ \pi /2 $
D) 1
Show Answer
Answer:
Correct Answer: B
Solution:
Limit $ =\underset{x\to 0}{\mathop{lim}}( \frac{\cos (\pi {{\cos }^{2}}x).\pi .2\cos x(-\sin x)}{2x} ) $ $ =\underset{x\to 0}{\mathop{lim}},\pi \cos (\pi {{\cos }^{2}}x).\cos x.( \frac{-\sin x}{x} ) $ $ =\pi (-1).1.(-1)=\pi $ .
BETA
