Question

Let $f(x) = 4$ and $f'(x) = 4$, then $\lim_{x \rightarrow 2}\frac{xf(2) - 2f(x)}{x - 2}$ equals

• A. 2
• B. – 2
• C. – 4
• D. 3

Answer 1

Answer: (C)

– 4

Answer 2

$y = \lim_{x \rightarrow 2}\frac{xf(2) - 2f(x)}{x - 2}$

⇒ $y = \lim_{x \rightarrow 2}\frac{xf(2) - 2f(2) + 2f(2) - 2f(x)}{x - 2}$

⇒ $y = \lim_{x \rightarrow 2}\frac{- 2f(x) + 2f(2) + xf(2) - 2f(2)}{(x - 2)}$

⇒ $y = \lim_{x \rightarrow 2} - 2\frac{\lbrack f(x) - f(2)\rbrack}{x - 2} + \lim_{x \rightarrow 2}\frac{f(2).(x - 2)}{(x - 2)}$

⇒ $y = - 2\lim_{x \rightarrow 2}\frac{f(x) - f(2)}{x - 2} + f(2)$

⇒$y = - 2\lim_{x \rightarrow 2}f^{'}(x) + f(2) = - 8 + 4 = - 4$.