Let $f:R \to R$ be a differentiable function and $f\left( 1 \right) = 4$. Then, the value of $\mathop {\lim }\limits_{x \to 1} \,\,\mathop \smallint \nolimits_4^{f\left( x \right)} \,\,\frac{{2\,t}}{{x - 1}}\,\,dt$〗is

JEE MATHEMATICS MCQ: LIMITS

1 Easy

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Application +4 | -1

Let

f:R \to R

be a differentiable function and

f\left( 1 \right) = 4

. Then, the value of

\lim\limits_{x \to 1} \,\,\int \nolimits_4^{f\left( x \right)} \,\,\frac{{2\,t}}{{x - 1}}\,\,dt

〗is

View answer and explanation

Correct option: A

8\,\,f'\,\,\left( 1 \right)

Option A (

8 f'(1)

) is correct because it is the result of applying L'Hopital's rule and the Fundamental Theorem of Calculus to the given limit.