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## Main Question or Discussion Point

What is an example where it's Riemann integrable int(f(t),t,a,x) but no derivative exists at certain pts?

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What is an example where it's Riemann integrable int(f(t),t,a,x) but no derivative exists at certain pts?

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HallsofIvy

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or [tex]f(x)=\left| x\right|[/tex]

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HallsofIvy

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mathwonk

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[tex]V_{3}[\tex]

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arildno

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[tex]F(x)=\sum_{n=0}^{\infty}\frac{\sin((n!)^{2}x)}{n!}[/tex]

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I'm not sure about this. Isn't [itex]F(x)= \int_0^x |t|dt[/itex] differentiable at 0? It is the piecewise function given by F(x)=x^2 for x>0 and F(x)=-x^2 for x>0 and F(0)=0.

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HallsofIvy

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Yes, you are right. That was an error on my part.

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