Question

Let $f (2) = 4$ and $f' (2) = 4$. Then $\displaystyle \lim_{x \to 2} \frac{xf(2) - 2 f(x)}{x-2}$ is given by

• A. 2
• B. -2
• C. -4
• D. 3

Answer 1

Answer: (C)

Apply L H Rule
We have, $\displaystyle \lim_{x \to2} \frac{xf\left(2\right)-2f\left(x\right)}{x-2} \left(\frac{0}{0}\right)$
$ = \displaystyle \lim_{x\to2} f\left(2\right) -2 f'\left(x\right) = f\left(2\right)-2f'\left(2\right) $
$= 4-2 \times4 = - 4$