Let $f:R \rightarrow R$ be a differentiable function and$f(1) = 4$. Then, the value of $\lim_{x \rightarrow 1}\frac{\int_{4}^{f\ (x)}{2t}}{x - 1}dt$, if $f^{'}(1) = 2$ is

Question

Dr. Abubacker · Accepted Answer

(a)
$\lim_{x \rightarrow 1}\frac{\int_{4}^{f\ (x)}{2t\ dt}}{x - 1} = \lim_{x \rightarrow 1}\frac{2f(x).f^{'}(x)}{1}$
$= 2f(1).f^{'}(1) = 16$

Q. Let $f:R \rightarrow R$ be a differentiable function and$f(1) = 4$. Then, the value of $\lim_{x \rightarrow 1}\frac{\int_{4}^{f\ (x)}{2t}}{x - 1}dt$, if $f^{'}(1) = 2$ is

Explanation

Reviewed by Dr. Abubacker

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