# Let f(x) be a differentiable function at

Question:

Let $f(x)$ be a differentiable function at $x=a$ with $f^{\prime}(a)=2$ and $f(a)=4$. Then lim $_{z \rightarrow a} \frac{x f(a)-a f(x)}{x-a}$ equals:

1. (1) $2 \mathrm{a}+4$

2. (2) $2 a-4$

3. (3) $4-2 a$

4. (4) $a+4$

Correct Option: , 3

Solution:

By L-H rule

$L=\lim _{x \rightarrow a} \frac{f(a)-a f^{\prime}(x)}{1}$

$\therefore L=4-2 a$