Question

The value of $k$ which makes $f(x)=\{\begin{array}{l}\sin x,x\ne 0\\ k,x=0\end{array}$ continuous at $x=0$, is:

• (A) $2$
• (B) $1$
• (C) $-1$
• (D) $0$

Answer 1

The Correct Option is D

Explanation:
$f(x)$ is Continuous at $x=0$$\Rightarrow \underset{x\to 0^{+}}{lim}f(x)=\underset{x\to 0^{-}}{lim}f(x)=f(0)$$\Rightarrow \underset{x\to 0^{+}}{lim}\sin x=\underset{x\to 0^{-}}{lim}\sin x=k$$\Rightarrow \underset{h\to 0}{lim}\sin (0+h)=\underset{h\to 0}{lim}\sin (0-h)=k$$\Rightarrow k=0$Hence, the correct option is (B).