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Continuity — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsContinuity2 Marks
MCQ
Let $f(x)=\left\{\begin{array}{ll}\frac{\sin \pi x}{5 x} ; & x \neq 0 \\ k ; & x=0\end{array}\right.$.If $f(x)$ is continuous at $x=0$, then $k =$
  • ✓
    $\frac{\pi}{5}$
  • B
    $\frac{5}{\pi}$
  • C
    1
  • D
    $0$
✓

Answer

Correct option: A.
$\frac{\pi}{5}$
(A)
Since $f (x)$ is continuous at $x=0$.
$\therefore \quad f (0)=\lim _{x \rightarrow 0} f (x)$
$\Rightarrow k =\lim _{x \rightarrow 0} \frac{\sin \pi x}{5 x}$
$\Rightarrow k =\lim _{x \rightarrow 0}\left(\frac{\sin \pi x}{\pi x}\right) \cdot \frac{\pi}{5}$
$\Rightarrow k =(1) \cdot \frac{\pi}{5}$
$\Rightarrow k =\frac{\pi}{5}$

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