Question

Let $f$ be real valued function such that $f\left(2\right)=2$ and $f^{\prime }\left(2\right)=1$, then $\underset{x\to 2}{lim}\underset{2}{\overset{f\left(x\right)}{\int }}\frac{4t^3}{x-2}dt$ equals

• A. $32$
• B. $8$
• C. $12$
• D. $6$

Answer 1

The correct option is A $32$

$\underset{x\to 2}{lim}\underset{2}{\overset{f\left(x\right)}{\int }}\frac{4t^3}{x-2}dt=\underset{x\to 2}{lim}\frac{\left[f\right(x){]}^4-16}{x-2}$
$=\underset{x\to 2}{lim}\frac{4\left[f\right(x\left){]}^3{f}^{\prime }\right(x)}{1}=32$