Functions Question 217
Question: The value of $ \underset{x\to 0}{\mathop{\lim }},\frac{x\cos x-\log (1+x)}{x^{2}} $ is
[RPET 1999]
Options:
A) ½
B) 0
C) 1
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ \underset{x\to 0}{\mathop{\lim }},\frac{x\cos x-\log (1+x)}{x^{2}} $ , $ ( \frac{0}{0}form ) $ Applying L-Hospital?s rule, we have $ \underset{x\to 0}{\mathop{\lim }}\frac{\cos x-x\sin x-\frac{1}{x+1}}{2x} $ , $ ( \frac{0}{0}form ) $ $ =\underset{x\to 0}{\mathop{\lim }}\frac{-\sin x-\sin x-x\cos x+\frac{1}{{{(x+1)}^{2}}}}{2}=\frac{1}{2} $ .
BETA
