Functions Question 85
Question: $ \underset{x\to 0}{\mathop{\lim }},\frac{{{(1+x)}^{1/2}}-{{(1-x)}^{1/2}}}{x}= $
[Roorkee 1979; RPET 1996]
Options:
A) 0
B) 1/2
C) 1
D) ?1
Show Answer
Answer:
Correct Answer: C
Solution:
Multiply function by $ \frac{{{(1+x)}^{1/2}}+{{(1-x)}^{1/2}}}{{{(1+x)}^{1/2}}+{{(1-x)}^{1/2}}} $ and solve. Aliter : Apply L-Hospital?s rule, $ \underset{x\to 0}{\mathop{\lim }}\frac{{{(1+x)}^{1/2}}-{{(1-x)}^{1/2}}}{x}=\underset{x\to 0}{\mathop{\lim }}\frac{1}{2\sqrt{1+x}}+\frac{1}{2\sqrt{1-x}}=1 $ .
BETA
