Let $f:R \to R$ be a differentiable function such that $f\left( 2 \right) = 2$. Then, the value of $\mathop {\lim }\limits_{x \to 2} \mathop \smallint \limits_2^{f\left( x \right)} \frac{{4\;{t^3}}}{{x - 2}}dt$, is

JEE MATHEMATICS MCQ: LIMITS

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Application +4 | -1

Let

f:R \to R

be a differentiable function such that

f\left( 2 \right) = 2

. Then, the value of

\lim\limits_{x \to 2} \int \limits_2^{f\left( x \right)} \frac{{4\;{t^3}}}{{x - 2}}dt

, is

View answer and explanation

Correct option: C

32f'\left( 2 \right)

Option C (

32f'(2)

) is correct because it is the result of applying L'Hopital's rule and the fundamental theorem of calculus to the given limit.

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