Which of the following is differentiable at $x=0 ?$

Question

Aicharya · Accepted Answer

At $x=0$, RHD $\sin |x|-|x|=\lim _{h ightarrow 0} \frac{(\sin |h|-|h|-(0)}{h}$ $\begin{aligned} & =\lim _{h ightarrow 0}\left(\frac{\sin h}{h}-1ight) \ & =1-1=0\end{aligned}$ LHD of $\sin |x|-|x|=\lim _{h ightarrow 0} \frac{(\sin |-h|-|-h|)}{-h}=0$ $\begin{aligned} & =\lim _{h ightarrow 0}\left[\left(\frac{\sin h}{-h}ight)+1ight] \ & =0\end{aligned}$ $L H D=R H D$ $	herefore \sin |x|-|x|$ is differentiable at $x=0$

Which of the following is differentiable at $x=0 ?$

Solution