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InterviewSolution
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Evaluate :\(\lim\limits_{x \to 0}\frac{log(6+x)-log(6-x)}{x}\) |
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Answer» \(\lim\limits_{x \to 0}\frac{log(1+\frac{x}{6})-log6(1-\frac{x}{6})}{x}\) = \(\lim\limits_{x \to 0}\frac{[log6+log(1+\frac{x}{6}]-[log6+log(1-\frac{x}{6})]}{x}\) = \(\lim\limits_{x \to 0}[\frac{log(1+\frac{x}{6})}{x}-\frac{log(1-\frac{x}{6})}{x}]\) = \(\lim\limits_{x \to 0}.\frac{1}{6}\frac{log(1+\frac{x}{6})}{\frac{x}{6}}+\lim\limits_{x \to 0}.\frac{1}{6}\frac{log(1-\frac{x}{6})}{(-\frac{x}{6})}]\) = \(\frac{1}{6}\times1+\frac{1}{6}\times1\,[∵ \lim\limits_{x \to 0}\frac{log(1+x)}{x}=\lim\limits_{x \to 0}\frac{log(1-x)}{-x}=1]\) = 0 |
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