Functions Question 347
Question: If $ f(x)= \begin{cases} \frac{1-\sin x}{\pi -2x}, & x\ne \frac{\pi }{2} \\ ,\lambda ,, & x=\frac{\pi }{2} \\ \end{cases} . $ , be continuous at $ x=\pi /2, $ then value of $ \lambda $ is
[RPET 2002]
Options:
A) ?1
B) 1
C) 0
D) 2
Show Answer
Answer:
Correct Answer: C
Solution:
$ f(x) $ is continuous at $ x=\frac{\pi }{2} $ , then $ \underset{x\to \pi /2}{\mathop{\lim }},f(x)=f(0) $ or $ \lambda =\underset{x\to \pi /2}{\mathop{\lim }},\frac{1-\sin x}{\pi -2x} $ , $ ( \frac{0}{0}\text{ form} ) $ Applying L-Hospital?s rule, $ \lambda =\underset{x\to \pi /2}{\mathop{\lim }},\frac{-\cos x}{-2} $
Þ $ \lambda =\underset{x\to \pi /2}{\mathop{\lim }},\frac{\cos x}{2}=0. $
BETA
