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प्रश्न
Write the points where f (x) = |loge x| is not differentiable.
उत्तर
Given:
Clearly
(LHD at x = 1)
\[ = - \lim_{x \to 1^-} \frac{\log x}{x - 1}\]
\[ = - \lim_{h \to 0} \frac{\log (1 - h)}{1 - h - 1}\]
\[ = - \lim_{h \to 0} \frac{\log (1 - h)}{- h} \]
\[ = - 1\]
(RHD at x=1)
\[= \lim_{x \to 1^+} \frac{\log x - \log 1}{x - 1}\]
\[ = \lim_{x \to 1^+} \frac{\log x}{x - 1}\]
\[ {= \lim_{h \to 0}}_{} \frac{\log (1 + h)}{1 + h - 1}\]
\[ = \lim_{h \to 0} \frac{\log (1 + h)}{h}\]
\[ = 1\]
Thus, (LHD at x =1) ≠ (RHD at x =1)
So,
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