Question

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

• A. 2
• B. -2
• C. -4
• D. 3

Answer 1

The correct option is C

-4

$\underset{x\to 2}{lim}\frac{xf\left(2\right)-2f\left(x\right)}{x-2}=\underset{x\to 2}{lim}\frac{xf\left(2\right)-2f^{\prime }\left(x\right)}{1}\text{using L-Hospital's rule}=f\left(2\right)-2f^{\prime }\left(2\right)=4-2\times 4=-4$