The value of displaystyle limx → 2 ∫ limitsx2(3t2/x-2)dt is

Question

The value of displaystyle limx → 2 ∫ limitsx2(3t2/x-2)dt is (A) 10 (B) 12 (C) 8 (D) 16

Tardigrade Admin · Accepted Answer

displaystyle lim x arrow 2 ∫2x (3 t2/(x-2)) d t =( displaystyle lim x arrow 2 ∫2x 3 t2 d t/ displaystyle lim x arrow 2(x-2)) =( displaystyle lim x arrow 2 3 x2/1) [using L' Hospital's rule] =3 ×(2)2=12

Q. The value of $x \to 2 lim$ $2 \int x$ $\frac{3 t ^{2}}{x - 2} d t$ is

10

12

8

16

$x \to 2 lim \int_{2}^{x} \frac{3 t ^{2}}{( x - 2 )} d t$
$= \frac{x \to 2 lim \int _{2}^{x} 3 t ^{2} d t}{x \to 2 lim ( x - 2 )}$
$= \frac{x \to 2 lim 3 x ^{2}}{1}$ [using L' Hospital's rule]
$= 3 \times (2)^{2} = 12$

Q. The value of x→2lim​ 2∫x​x−23t2​dt is

10

12

8

16

x→2lim​∫2x​(x−2)3t2​dt =x→2lim​(x−2)x→2lim​∫2x​3t2dt​ =1x→2lim​3x2​ [using L' Hospital's rule] =3×(2)2=12

Q. The value of $x \to 2 lim$ $2 \int x$ $\frac{3 t ^{2}}{x - 2} d t$ is

$x \to 2 lim \int_{2}^{x} \frac{3 t ^{2}}{( x - 2 )} d t$
$= \frac{x \to 2 lim \int _{2}^{x} 3 t ^{2} d t}{x \to 2 lim ( x - 2 )}$
$= \frac{x \to 2 lim 3 x ^{2}}{1}$ [using L' Hospital's rule]
$= 3 \times (2)^{2} = 12$