Functions Question 596
Question: $ \underset{x\to 1}{\mathop{\lim }},(1-x)\tan ( \frac{\pi x}{2} )= $
[IIT 1978, 84; RPET 1997, 2001; UPSEAT 2003; Pb. CET 2003]
Options:
A) $ \frac{\pi }{2} $
B) $ \pi $
C) $ \frac{2}{\pi } $
D) 0
Show Answer
Answer:
Correct Answer: C
Solution:
$ \underset{x\to 1}{\mathop{\lim }}(1-x)\tan ,( \frac{\pi x}{2} ) $ . Put $ 1-x=y $ as $ x\to 1,y\to 0 $
Thus $ \underset{y\to 0}{\mathop{\lim }},y\tan \frac{\pi (1-y)}{2}=\underset{y\to 0}{\mathop{\lim }},\frac{2}{\pi }. $ $ \frac{\pi y}{2}\tan ( \frac{\pi y}{2} )=\frac{2}{\pi }\times 1=\frac{2}{\pi }. $
BETA
