Let $f\left( x \right)$ be a differentiable function such that $f\left( 1 \right) = 2$. If $\mathop {\lim }\limits_{x \to 1} \,\,\mathop \smallint \limits_2^{f\left( x \right)} \,\,\frac{{2t}}{{x - 1}}\,\,dt = 4$, then the value of $f'\left( 1 \right)$ is

JEE MATHEMATICS MCQ: LIMITS

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Let

f\left( x \right)

be a differentiable function such that

f\left( 1 \right) = 2

. If

\lim\limits_{x \to 1} \,\,\int \limits_2^{f\left( x \right)} \,\,\frac{{2t}}{{x - 1}}\,\,dt = 4

, then the value of

f'\left( 1 \right)

View answer and explanation

Correct option: A

\mathrm{1}

Option A (1) is correct because applying L'Hopital's rule and the Fundamental Theorem of Calculus leads to

f'(1) = 1