Question:
Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be a function such that $f(2)=4$ and
$f^{\prime}(2)=1 .$ Then, the value of $\lim _{x \rightarrow 2} \frac{x^{2} f(2)-4 f(x)}{x-2}$ is
equal to :
Correct Option: , 4
Solution:
Apply L'Hopital Rule
$\lim _{x \rightarrow 2}\left(\frac{2 x f(2)-4 f^{\prime}(x)}{1}\right)$
$=\frac{4(4)-4}{1}=12$