Let $f:R \to R$ be a differentiable function such that $f\left( 3 \right) = 3,f'\left( 3 \right) = \frac{1}{2}$, Then, the value of $\mathop {\lim }\limits_{x \to 3} \,\frac{{\mathop \smallint \nolimits_3^{f\left( x \right)} 2{t^3}\,dt}}{{x - 3}}$ 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( 3 \right) = 3,f'\left( 3 \right) = \frac{1}{2}

, Then, the value of

\lim\limits_{x \to 3} \,\frac{{\int \nolimits_3^{f\left( x \right)} 2{t^3}\,dt}}{{x - 3}}

View answer and explanation

Correct option: C

Option C (27) is correct because applying L'Hopital's rule and the given values of f(3) and f'(3) leads to the result 27.