question_answer

If \[f(x)=\left\{ \begin{align}   & \frac{{{x}^{4}}-16}{x-2},\,\,\text{when}\,x\ne 2 \\  & \,\,\,\,\,\,\,\,\,\,\,\,\,16,\,\text{when}\,x=2 \\ \end{align} \right.\], then                    [AISSE 1984]

A)            \[f(x)\]is continuous at \[x=2\]

B)            \[f(x)\]is discountinous at \[x=2\]

C)            \[\underset{x\to 2}{\mathop{\lim }}\,f(x)=16\]

D)            None of these