Question

If the function $f\left(x\right)=\{\begin{array}{ccc}\frac{kcosx}{\pi -2x},& when& x\ne \frac{\pi }{2}\\ 3,& when& x=\frac{\pi }{2}\end{array}$ be continuous at $x-\frac{\pi }{2}$, then k=

• A. 3
• B. 6
• C. 12
• D. None of these

Answer 1

The correct option is B 6

$f\left(\frac{\pi }{2}\right)=3$. Since f(x) is continuous at $x=\frac{\pi }{2}$
$\Rightarrow {lim}_{x\to \pi /2}\left(\frac{kcosx}{\pi -2x}\right)=f\left(\frac{\pi }{2}\right)\Rightarrow \frac{k}{2}=3\Rightarrow k=6$