Functions Question 637
Question: If the function $ f(x)= \begin{cases} & \frac{k\cos x}{\pi -2x},\text{when }x\ne \frac{\pi }{2} \\ & 3,\ \ \ \ \ \ \ \ \ \text{when }x=\frac{\pi }{2} \\ \end{cases} . $ be continuous at $ x=\frac{\pi }{2} $ , then k =
Options:
A) 3
B) 6
C) 12
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ f,(\pi /2)=3 $ . Since $ f(x) $ is continuous at $ x=\pi /2 $
$ \Rightarrow ,\underset{x\to \pi /2}{\mathop{\lim }}( \frac{k\cos x}{\pi -2x} )=f( \frac{\pi }{2} )\Rightarrow \frac{k}{2}=3\Rightarrow k=6. $
BETA
