Functions Question 241
Question: The value of $ \underset{x\to 0}{\mathop{\lim }}
[ \frac{\sqrt{a+x}-\sqrt{a-x}}{x} ] $ is [Karnataka CET 2001]
Options:
A) 1
B) 0
C) $ \sqrt{a} $
D) $ 1/\sqrt{a} $
Show Answer
Answer:
Correct Answer: D
Solution:
$ \underset{x\to 0}{\mathop{lim}},[ \frac{\sqrt{a+x}-\sqrt{a-x}}{x} ] $ $ =\underset{x\to 0}{\mathop{lim}}[ \frac{(\sqrt{a+x}-\sqrt{a-x})(\sqrt{a+x}+\sqrt{a-x})}{x(\sqrt{a+x}+\sqrt{a-x})} ] $ $ =\underset{x\to 0}{\mathop{lim}}[ \frac{2x}{x(\sqrt{a+x}+\sqrt{a-x})} ]=\frac{2}{\sqrt{a}+\sqrt{a}}=\frac{1}{\sqrt{a}} $ .
BETA
