Functions Question 64
Question: $ \underset{x\to 0}{\mathop{\lim }},[ \frac{1}{x}-\frac{\log (1+x)}{x^{2}} ] $ =
Options:
A) ½
B) ?1/2
C) 1
D) ?1
Show Answer
Answer:
Correct Answer: A
Solution:
Expand $ \log ,(1+x) $ and then solve. Aliter : Apply L-Hospital?s rule, $ \underset{x\to 0}{\mathop{\lim }}[ \frac{x-\log ,(1+x)}{x^{2}} ] $ $ =\underset{x\to 0}{\mathop{\lim }},\frac{1-\frac{1}{1+x}}{2x} $ $ =\underset{x\to 0}{\mathop{\lim }},\frac{1}{2},{{( \frac{1}{1+x} )}^{2}}=\frac{1}{2}. $
BETA
