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Question: The value of \(\lim_{x \rightarrow 2}\frac{3^{x/2} - 3}{3^{x} - 9}\) is...

The value of lim⁡x→23x/2−33x−9\lim_{x \rightarrow 2}\frac{3^{x/2} - 3}{3^{x} - 9} is

A

0

B

13\frac{1}{3}

C

16\frac{1}{6}

D

ln⁡3\ln 3

Answer

16\frac{1}{6}

Explanation

Solution

lim⁡x→23x/2−3(3x/2)2−(3)2\lim_{x \rightarrow 2}\frac{3^{x/2} - 3}{(3^{x/2})^{2} - (3)^{2}}=lim⁡x→2(3x/2−3)(3x/2−3)(3x/2+3)\lim_{x \rightarrow 2}\frac{(3^{x/2} - 3)}{(3^{x/2} - 3)(3^{x/2} + 3)}=16\frac{1}{6}.