Functions Question 274
Question: If $ \underset{x\to 0}{\mathop{\lim }},\frac{\log (3+x),-\log (3-x)}{x}=k,, $ then the value of k is
[AIEEE 2003]
Options:
A) 0
B) $ -\frac{1}{3} $
C) $ \frac{2}{3} $
D) $ -\frac{2}{3} $
Show Answer
Answer:
Correct Answer: C
Solution:
$ \underset{x\to 0}{\mathop{\lim }},\frac{\log (3+x)-\log (3-x)}{x}=k $ By L-Hospital?s rule, $ \underset{x\to 0}{\mathop{\lim }},\frac{\frac{1}{3+x}+\frac{1}{3-x}}{1}=k $
Þ $ \frac{2}{3}=k $ .
BETA
