Limits Continuity And Differentiability Question 31
Question: If the function $ f(x)= \begin{cases} & \frac{k\cos x}{\pi -2x},whenx\ne \frac{\pi }{2} \\ & 3,whenx=\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
