Question

If $f(2) = 4$ and $f'(2) = 1$, then $\displaystyle\lim_{x \to 2} \frac{xf (2) - 2 f (x) }{x -2}$ is equal to

• A. -2
• B. 1
• C. 2
• D. 3

Answer 1

Answer: (C)

2

Answer 2

The value of $\displaystyle\lim _{x \rightarrow 2} \frac{x f(2)-2 f(x)}{x-2}$
$=\displaystyle\lim _{x \rightarrow 2} \frac{x f(2)-2 f(2)+2 f(2)-2 f(x)}{x-2}$
$=\displaystyle\lim _{x \rightarrow 2} \frac{(x-2) f(2)}{x-2}-2 \displaystyle\lim _{x \rightarrow 2} \frac{f(x)-f(2)}{x-2}$
$=f(2)-2 f'(2)=4-2 \times 1=2$