A) 1
B) ?1
C) 0
D) \[\infty \]
Correct Answer: A
Solution :
\[\underset{x\to 1}{\mathop{\lim }}\,\,\,\frac{\log \,[(x-1)+1]}{x-1}=1.\] Aliter : Apply L-Hospital?s rule, \[\underset{x\to 1}{\mathop{\lim }}\,\frac{\log x}{x-1}=\underset{x\to 1}{\mathop{\lim }}\,\frac{\frac{1}{x}}{1}=1\]
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