Question

\(\lim _{x \rightarrow 1}\left(\frac{1}{\ln x}-\frac{1}{(x-1)}\right)\)
(A) Does not exist
(B) 1
(C) \(\frac{1}{2}\)
(D) 0

Answer 1

Ans: (C)
Hint : It \(\left(\frac{1}{x \rightarrow 1}-\frac{1}{x-1}\right)=\operatorname{lt}_{x \rightarrow 1} \frac{(x-1)-\ln x}{(x-1) \ln x}=\frac{1}{2}\)
Using L.H. rule twice