Consider the following functions : 1. f(x)=\ array lll (1)/(x) & if...

$f(x)=$\begin{cases}\frac{1}{x} & x \neq 0 \\ 0 & x=0\end{cases}as there is a discontinuity at $\mathrm{x}=0$, so function is not differentiable at $\mathrm{x}=0\begin{aligned} & f(x)=\left\{\begin{array}{cc} 2 x+5 & x > 0 \\ x^2+2 x+5 & x \leq 0 \end{array}\right. \\ & f(0)=5 \\ & \operatorname{LHD}=\lim _{\mathrm{x} \rightarrow 0^{-}} \frac{\mathrm{f}(\mathrm{x})-\mathrm{f}(0)}{\mathrm{x}-0} \\ & =\lim _{x \rightarrow 0} \frac{x^2+2 x+5-5}{x}=\lim _{x \rightarrow 0} x+2=2 \\ & R H D=\lim _{x \rightarrow 0^{+}} \frac{f(x)-f(0)}{x-0} \\ & =\lim _{x \rightarrow 0} \frac{2 x+5-5}{x}=2 \end{aligned}$$\therefore$ It is differentiable at $\mathrm{x}=0\therefore$ Only (2) is differentiable at $\mathrm{x}=0$