If f: R → R is a differentiable function and f(2) = 6, then displaystyle lim limitsx → 2 ∫f(x)6 (2tdt/(x-2)) is :

Question

If f: R → R is a differentiable function and f(2) = 6, then displaystyle lim limitsx → 2 ∫f(x)6 (2tdt/(x-2)) is : (A) 0 (B) 2 f'(2) (C) 12 f '(2) (D) 24 f '(2)

Tardigrade Admin · Accepted Answer

displaystyle limx→2 (∫f(x)6 2t dt /x-2) L Hopital Rule displaystyle limx→2 (2f (x)f '(x)/1) = 2f (2) f '(2) 12f '(2)

Q. If f : R $\to$ R is a differentiable function and $f (2) = 6$ , then $x \to 2 lim \int_{6}^{f (x)} \frac{2 t d t}{( x - 2 )}$ is :

$0$

$2 f^{'} (2)$

$12 f^{'} (2)$

$24 f^{'} (2)$

$lim x \to 2 \frac{\int _{6}^{f (x)} 2 t d t}{x - 2}$
L Hopital Rule
$x \to 2 lim \frac{2 f ( x ) f ^{'} ( x )}{1} = 2 f (2) f^{'} (2) 12 f^{'} (2)$

Q. If f : R → R is a differentiable function and f(2)=6, then x→2lim​∫6f(x)​(x−2)2tdt​ is :

0

2f′(2)

12f′(2)

24f′(2)

limx→2x−2∫6f(x)​2tdt​ L Hopital Rule x→2lim​12f(x)f′(x)​=2f(2)f′(2)12f′(2)

Q. If f : R $\to$ R is a differentiable function and $f (2) = 6$ , then $x \to 2 lim \int_{6}^{f (x)} \frac{2 t d t}{( x - 2 )}$ is :

$0$

$2 f^{'} (2)$

$12 f^{'} (2)$

$24 f^{'} (2)$

$lim x \to 2 \frac{\int _{6}^{f (x)} 2 t d t}{x - 2}$
L Hopital Rule
$x \to 2 lim \frac{2 f ( x ) f ^{'} ( x )}{1} = 2 f (2) f^{'} (2) 12 f^{'} (2)$