Question

Let $f\left(x\right)$ be a differentiable function at $x=a$ with $f^{\prime }\left(a\right)=2$ and $f\left(a\right)=4$. Then $\underset{x\to a}{lim}\frac{xf\left(a\right)-af\left(x\right)}{x-a}$ equals:

• A. $2a+4$
• B. $2a-4$
• C. $4-2a$
• D. $a+4$

Answer 1

The correct option is C $4-2a$

$L=\underset{x\to a}{lim}\frac{xf\left(a\right)-af\left(x\right)}{x-a}$
By L'Hospital rule
$L=\underset{x\to a}{lim}\frac{f\left(a\right)-a{f}^{\prime }\left(x\right)}{1}$
$\therefore L=4-2a$