Question

Let f(x) = 4 and f’(x) = 4. Then $\underset{x\to 0}{lim}\frac{xf\left(2\right)-2f\left(x\right)}{x-2}$ is given by

• A. 2
• B. -2
• C. -4
• D. 3

Answer 1

The correct option is C

-4

Apply L'Hospital Rule, we have,

$\underset{x\to 0}{lim}\frac{xf\left(2\right)-2f\left(x\right)}{x-2}\left(\frac{0}{0}\right)$

$\underset{x\to 0}{lim}f\left(2\right)-2f^{\prime }\left(x\right)$
$=f\left(2\right)-2f^{\prime }\left(0\right)=4-2\times 4=-4$