Q55 / 155 · WBJEE 2022 · Mathematics

$\lim _{x \rightarrow 0}\left(\frac{1}{x} \ln \sqrt{\frac{1+x}{1-x}}\right)$ is

  • A
    $1 / 2$
  • B
    0
  • Correct answer
    C
    1
  • D
    does not exist

Solution

$\lim _{x \rightarrow 0} \frac{1 / 2(\ln (1+x)-\ln (1-x))}{x}$ $=\frac{1}{2} \lim _{x \rightarrow 0}\left(\frac{1}{1+x}+\frac{1}{1-x}\right)=1$

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

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