Q103 / 155 · WBJEE 2020 · Mathematics

$\lim _{x \rightarrow 1}\left(\frac{1}{\ln x}-\frac{1}{(x-1)}\right)$

  • A
    Does not exist
  • B
    1
  • Correct answer
    C
    $\frac{1}{2}$
  • D
    0

Solution

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

Hence, the correct answer is option: 'C'.

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