Limits Continuity And Differentiability Question 36
Question: What is $ \underset{x\to 0}{\mathop{\lim }}\frac{\sqrt{1+x}-1}{x} $ equal to?
Options:
A) 0
B) $ \frac{1}{2} $
C) 1
D) $ -\frac{1}{2} $
Show Answer
Answer:
Correct Answer: B
Solution:
$ \underset{x\to 0}{\mathop{\lim }}\frac{\sqrt{1+x}-1}{x} $
$ =\underset{x\to 0}{\mathop{\lim }}\frac{\sqrt{1+x}-1}{x}\times \frac{\sqrt{1+x}+1}{\sqrt{1+x}+1} $
$ =\underset{x\to 0}{\mathop{\lim }}\frac{1+x-1}{x[ \sqrt{1+x}+1 ]} $
$ =\underset{x\to 0}{\mathop{\lim }}\frac{1}{\sqrt{1+x}+1}=\frac{1}{\sqrt{1+0}+1}=\frac{1}{2} $
BETA
