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Question: Answered & Verified by Expert
If $\lim _{x \rightarrow 0} \frac{\log (3+x)-\log (3-x)}{x}=k$, the value of $k$ is
MathematicsLimitsJEE MainJEE Main 2003
Options:
  • A
    $-\frac{2}{3}$
  • B
    0
  • C
    $-\frac{1}{3}$
  • D
    $\frac{2}{3}$
Solution:
2137 Upvotes Verified Answer
The correct answer is:
$\frac{2}{3}$
$\operatorname{Lim}_{x \rightarrow 0} \frac{\log (3+x)-\log (3-x)}{x}=K$ (by L'Hospital rule)
$\operatorname{Lim}_{x \rightarrow 0} \frac{\frac{1}{3+x}-\frac{-1}{3-x}}{1}=K \quad \therefore \frac{2}{3}=\mathrm{K}$

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