MCQ
If $f(x)=\left\{\begin{array}{cc}\frac{\sin 3 x}{x}, & x \neq 0 \\ \frac{k}{2}, & x=0\end{array}\right.$ is continuous at $x=0$, then the value of $k$ is
  • A
    12
  • B
    9
  • 6
  • D
    2

Answer

Correct option: C.
6
(C)
Since $f (x)$ is continuous at $x=0$.
$\therefore \quad f (0)=\lim _{x \rightarrow 0} f (x)$
$\Rightarrow \frac{ k }{2}=\lim _{x \rightarrow 0} \frac{\sin 3 x}{x}=\lim _{x \rightarrow 0} \frac{\sin 3 x}{3 x} \cdot 3$
$\Rightarrow \frac{k}{2}=3 \Rightarrow k=6$

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