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प्रश्न
Write an example of a function which is everywhere continuous but fails to differentiable exactly at five points.
उत्तर
The above function is continuous everywhere but not differentiable at x = 0, 1, 2, 3 and 4
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संबंधित प्रश्न
Examine the following function for continuity:
f (x) = x – 5
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(i) \[f\left( x \right) = \begin{cases}\left| x \right| \cos\left( \frac{1}{x} \right), & x \neq 0 \\ 0 , & x = 0\end{cases}at x = 0\]
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(ii) \[f\left( x \right) = \left\{ \begin{array}{l}x^2 \sin\left( \frac{1}{x} \right), & x \neq 0 \\ 0 , & x = 0\end{array}at x = 0 \right.\]
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In each of the following, find the value of the constant k so that the given function is continuous at the indicated point; \[f\left( x \right) = \begin{cases}\frac{x^2 - 25}{x - 5}, & x \neq 5 \\ k , & x = 5\end{cases}\]at x = 5
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