If f: R → R is a differentiable function and f(2) = 6, then lim_x → 2 int_6^f(x) (2t dt)/((x-2)) is

If f: R → R is a differentiable function and f(2) = 6, then… — JEE Main 2019 Mathematics PYQ

JEE Main 2019 · 9 Apr · Shift II

f: R \to R

is a differentiable function and

f(2) = 6

, then

\lim_{x \to 2} \int_{6}^{f(x)} \frac{2t\, dt}{(x-2)}

A.
$12f'(2)$
B.
$0$
C.
$24f'(2)$
D.
$2f'(2)$

Show answer and solution

Correct option: A

Solution

Using L'Hôpital's rule (or Leibniz rule), differentiate numerator and denominator with respect to x. The numerator is ∫₆^f(x) 2t dt, whose derivative with respect to x is 2f(x)·f'(x) by the Fundamental Theorem of Calculus. The denominator (x−2) differentiates to 1. Taking the limit as x→2, with f(2)=6, gives 2·f(2)·f'(2) = 2·6·f'(2) = 12f'(2).

[JEE Main 2019 · 9 Apr · Shift II]

Practise Limits Continuity and Differentiability the way it is asked

A timed set of real JEE Main Limits Continuity and Differentiability questions, graded as the exam grades. No sign-up.

Start a Limits Continuity and Differentiability test

More: all JEE Main Limits Continuity and Differentiability questions · JEE Main 2019 · Mathematics chapter list

JEE Main 2019 Mathematics question on Limits Continuity and Differentiability