If f is twice differentiable function then $\lim\limits_{h \rightarrow 0} \frac{f(a+h)-2 f(a)+f(a-h)}{h^2}$ is

f''(a)

$\lim\limits_{h \rightarrow 0} \frac{f(a+h)-2 f(a)+f(a-h)}{h^2} ~~~\left(\frac{0}{0}\right)$

$=\lim\limits_{h \rightarrow 0} \frac{f'(a+h)-f'(a-h)}{2 h} ~~~\left(\frac{0}{0}\right)$

$=\lim\limits_{h \rightarrow 0} \frac{f''(a+h)+f''(a-h)}{2}=f''(a)$

Hence (2) is correct answer.