_ x 2 3^ x +3^ 3-x -12 3^ -x / 2 -3^ 1-x is equal to - Vidyadip

MCQ

$\lim\limits_{x \rightarrow 2} \frac{3^{x}+3^{3-x}-12}{3^{-x / 2}-3^{1-x}}$ is equal to

A
$25$
✓
$36$
C
$49$
D
$42$

✓

Answer

Correct option: B.

$36$

b
$\lim _{x \rightarrow 2} \frac{3^{x}+3^{3-x}-12}{3^{-x / 2}-3^{1-x}} \Rightarrow \lim _{x \rightarrow 2} \frac{3^{2 x}-12.3^{x}+27}{3^{x / 2}-3}$

$=\lim _{x \rightarrow 2} \frac{\left(3^{x}-9\right)\left(3^{x}-3\right)}{\left(3^{x / 2}-3\right)}$

$=\lim _{x \rightarrow 2} \frac{\left(3^{x / 2}+3\right)\left(3^{x / 2}-3\right)\left(3^{x}-3\right)}{\left(3^{x / 2}-3\right)}$

$=36$

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