Let $f:R \rightarrow R$ be a differentiable function having$f(2) = 6,\ f^{'}(2) = \left( \frac{1}{48} \right)$. Then, $\lim_{x \rightarrow 2}\frac{\int_{6}^{f(x)}{4\ t^{3}\ dt}}{x - 2}$ is equals

Question

Dr. Abubacker · Accepted Answer

(a)
$\lim_{x ightarrow 2}\frac{\int_{6}^{f(x)}{4\ t^{3}\ dt}}{x - 2}\lim_{x ightarrow 2}{\frac{4\left\{ f(x) ight\}^{3}}{1}.f^{'}(x)}$
$= 4\left\{ f(2) ight\}^{3}.f^{'}(2)$
$= 4 	imes (6)^{3}.\frac{1}{48}$
$= 18$

Q. Let $f:R \rightarrow R$ be a differentiable function having$f(2) = 6,\ f^{'}(2) = \left( \frac{1}{48} \right)$. Then, $\lim_{x \rightarrow 2}\frac{\int_{6}^{f(x)}{4\ t^{3}\ dt}}{x - 2}$ is equals

Explanation

Reviewed by Dr. Abubacker

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