A) 0
B) 1/3
C) \[1/6\]
D) \[\ln 3\]
Correct Answer: C
Solution :
\[\underset{x\to 2}{\mathop{\lim }}\,\,\left( \frac{{{3}^{x/2}}-3}{{{3}^{x}}-9} \right)\] \[=\underset{x\to 2}{\mathop{\text{lim}}}\,\,\,\left( \frac{{{3}^{x/2}}-3}{{{({{3}^{x/2}})}^{2}}-{{3}^{2}}} \right)\] \[=\underset{x\to 2}{\mathop{\text{lim}}}\,\,\frac{1}{{{3}^{x/2}}+3}=\frac{1}{6}\].
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