Question

$\underset{x\to 2}{\lim }\frac{3^x+3^{3-x}-12}{3^{-x/2}-3^{1-x}}$ is equal to __________.

Answer 1

Answer: 36.00

$li{m}_{x\to 2}\frac{3^x+3^{3-x}-12}{3^{-x/2}-3^{1-x}}\Rightarrow li{m}_{x\to 2}\frac{3^{2x}-12.3^x+27}{3^{x/2}-3}$
$=li{m}_{x\to 2}\frac{\left(3^x-9\right)\left(3^x-3\right)}{\left(3^{x/2}-3\right)}$
$=li{m}_{x\to 2}\frac{\left(3^{x/2}+3\right)\left(3^{x/2}-3\right)\left(3^x-3\right)}{\left(3^{x/2}-3\right)}$
$=36$