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Continuity — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsContinuity2 Marks
MCQ
If the function $f(x)=\left\{\begin{array}{cc}\frac{k \cos x}{\pi-2 x}, & \text { when } x \neq \frac{\pi}{2} \\ 3, & \text { when } x=\frac{\pi}{2}\end{array}\right.$ is continuous at $x=\frac{\pi}{2}$, then $k =$
  • A
    3
  • ✓
    6
  • C
    9
  • D
    12
✓

Answer

Correct option: B.
6
(B)
Since $f (x)$ is continuous at $x=\frac{\pi}{2}$.
$\therefore \quad f \left(\frac{\pi}{2}\right)=\lim _{x \rightarrow \frac{\pi}{2}} f (x)$
$\Rightarrow 3=\lim _{x \rightarrow \frac{\pi}{2}}\left(\frac{ k \cos x}{\pi-2 x}\right)$
Applying L'Hospital rule on R.H.S., we get
$3=\lim _{x \rightarrow \frac{\pi}{2}} \frac{ k (-\sin x)}{-2}$
$\Rightarrow 3-\frac{ k }{2} \Rightarrow k -6$

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