Question

If $f\left(x\right)=\frac{\sin 3x}{\sin x},x\ne 0$ is continuous
$=K,x=0$
function, then $K=$

• A. $1$
• B. $3$
• C. $\frac{1}{3}$
• D. $0$

Answer 1

The correct option is B $3$

$f\left(x\right)$ is continuous if $\underset{x\to 0}{lim}f\left(x\right)=f\left(0\right)$

$\Rightarrow \underset{x\to 0}{lim}\frac{\sin 3x}{sinx}=K$

$\underset{x\to 0}{lim}\frac{3\cos 3x}{cosx}=K$

$\Rightarrow K=3$ [B]