Functions Question 229
Question: The value of $ \underset{x\to 2}{\mathop{\lim }},\frac{{3^{x/2}}-3}{3^{x}-9} $ is
[MP PET 2000]
Options:
A) 0
B) 1/3
C) $ 1/6 $
D) $ \ln 3 $
Show Answer
Answer:
Correct Answer: C
Solution:
$ \underset{x\to 2}{\mathop{\lim }}( \frac{{3^{x/2}}-3}{3^{x}-9} ) $ $ =\underset{x\to 2}{\mathop{lim}},( \frac{{3^{x/2}}-3}{{{({3^{x/2}})}^{2}}-3^{2}} ) $ $ =\underset{x\to 2}{\mathop{lim}}\frac{1}{{3^{x/2}}+3}=\frac{1}{6} $ .
BETA
