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I Need an example of piece wise function continuous but not differentiable. One of the functions has to be trigonometric and the other has to be exponential. Please

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Hint: Let $f(x)=\cos x$ for $x\le 0$ and let $f(x)=e^x$ for $x\gt 0$.

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$$f(x)=\left\{\begin{array}{ll}\cos(x)& x\leq 0\\e^x &x>0\end{array}\right.$$

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$$ \sin(|x|) $$ $$ \mathrm{e}^{-|x|} $$

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You may consider the function$$f(x)=\sin x$$ for $x<0$ and $$f(x)=e^{2x}-1$$ for $x>0$

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  • $\begingroup$ "the functions has to be trigonometric and the other has to be exponential" $\endgroup$ – Dario Jun 17 '14 at 6:31
  • $\begingroup$ @Dario- Yes, edited accordingly $\endgroup$ – freebird Jun 17 '14 at 6:32
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    $\begingroup$ This new one is not continuous (moreover it is not defined in 0). $\endgroup$ – Dario Jun 17 '14 at 6:32
  • $\begingroup$ @Dario- I don't know what is wrong with me today. I suppose it should be OK now. $\endgroup$ – freebird Jun 17 '14 at 6:36
  • $\begingroup$ Now it's fine :) $\endgroup$ – Dario Jun 17 '14 at 6:37

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