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