Functions Question 244
Question: $ \underset{x\to 1}{\mathop{\lim }},\frac{1+\cos \pi ,x}{{{\tan }^{2}}\pi ,x} $ is equal to
[AMU 2001]
Options:
A) 0
B) 1/2
C) 1
D) 2
Show Answer
Answer:
Correct Answer: B
Solution:
$ \underset{x\to 1}{\mathop{\lim }},\frac{(1+\cos \pi x)}{{{\tan }^{2}}\pi x}=\underset{x\to 1}{\mathop{\lim }},\frac{-\pi \sin \pi x}{2\pi \tan \pi x{{\sec }^{2}}\pi x} $ [Using L-Hospital?s rule] $ =\underset{x\to 1}{\mathop{\lim }},\frac{-1}{2}{{\cos }^{3}}\pi ,x $ $ =\frac{1}{2} $ .
BETA
