Question

lf the function $f\left(x\right)=\{\begin{array}{cc}\frac{\sin 3x}{x}& (x\ne 0)\\ \frac{k}{2}& (x=0)\end{array}$ is continuous at $x=0$, then $k$ is:

• A. 3
• B. 6
• C. 9
• D. 2

Answer 1

The correct option is B 6

Since $f\left(x\right)$ is continuous at $x=0$

LHL = RHL

$\underset{x\to 0^{-}}{Lim}f\left(x\right)=limx\to 0^{+}f\left(x\right)$

$\underset{x\to 0^{-}}{Lim}\frac{sin3x}{x}=limx\to 0^{+}\frac{k}{2}$

$\underset{x\to 0^{-}}{Lim}\frac{sin3x}{3x}\times 3=limx\to 0^{+}\frac{k}{2}$

$\Rightarrow 3=\frac{k}{2}$

Hence, $k=6$