WBJEE · Maths · Limits
\(\lim _{x \rightarrow 1}\left(\frac{1}{\ln x}-\frac{1}{(x-1)}\right)\)
- A Does not exist
- B 1
- C \(\frac{1}{2}\)
- D 0
Answer & Solution
Correct Answer
(C) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
Hint: \(\operatorname{lt}_{x \rightarrow 1}\left(\frac{1}{\ln x}-\frac{1}{x-1}\right)=\operatorname{lt}_{x \rightarrow 1} \frac{(x-1)-\ln x}{(x-1) \ln x}=\frac{1}{2}\) Using L.H. rule twice
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