Question

If f : R $\to$ R is a differentiable function and $f(2) = 6$, then $\displaystyle\lim\limits_{x \to 2} \int^{f(x)}_6 \frac{2tdt}{(x-2)}$ is :

• A. $0$
• B. $2 f'(2)$
• C. $12 f '(2)$
• D. $24 f '(2)$

Answer 1

Answer: (C)

$\displaystyle\lim{x\to2} \frac{\int^{f\left(x\right)}_{6} 2t dt }{x-2} $
L Hopital Rule
$ \displaystyle\lim_{x\to2} \frac{2f \left(x\right)f '\left(x\right)}{1} = 2f \left(2\right) f '\left(2\right) 12f '\left(2\right)$