If the function f(x) = l k x - 2x , when x 2 3, ; ; ; ; ; ; ; ; ;… - Vidyadip

MCQ

If the function $f(x) = \left\{ \begin{array}{l}\frac{{k\cos x}}{{\pi - 2x}},{\rm{when }}x \ne \frac{\pi }{2}\\3,\;\;\;\;\;\;\;\;\;{\rm{when }}x = \frac{\pi }{2}\end{array} \right.$ be continuous at $x = \frac{\pi }{2}$, then $ k =$

A
$3$
✓
$6$
C
$12$
D
None of these

✓

Answer

Correct option: B.

$6$

b
(b) $f\,(\pi /2) = 3$. Since $f(x)$ is continuous at $x = \pi /2$

$ \Rightarrow \,\mathop {\lim }\limits_{x \to \pi /2} \,\left( {\frac{{k\cos x}}{{\pi - 2x}}} \right) = f\left( {\frac{\pi }{2}} \right)\,\, $

$\Rightarrow \,\,\frac{k}{2} = 3\,\, \Rightarrow \,\,k = 6.$

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