Let $f:R \rightarrow R$ be a differentiable function such that $f(3) = 3,\ f^{'}(3) = \frac{1}{2}$, Then, the value of $\lim_{x \rightarrow 3}\frac{\int_{3}^{f(x)}{2t^{3}dt}}{x - 3}$ is

Question

Dr. Abubacker · Accepted Answer

(c)
$\lim_{x ightarrow 3}\frac{\int_{3}^{f(x)}{2t^{3}dt}}{x - 3} = \lim_{x ightarrow 3}\frac{2\left\lbrack f(x) ightbrack^{3}.f^{'}(x)}{1}$
$= 2\left\lbrack f(3) ightbrack^{3}.f^{'}(3) = {2 	imes 3}^{3} 	imes \frac{1}{2}\$
$= 27$

Q. Let $f:R \rightarrow R$ be a differentiable function such that $f(3) = 3,\ f^{'}(3) = \frac{1}{2}$, Then, the value of $\lim_{x \rightarrow 3}\frac{\int_{3}^{f(x)}{2t^{3}dt}}{x - 3}$ is

Explanation

Reviewed by Dr. Abubacker

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