Tuesday 28 February 2017

real analysis - a differentiable function but its derivative is discontinuous everywhere

Is there a function $f$: $\mathbb R\to \mathbb R$ such that $f$ is differentiable everywhere but $f'$ is discontinuous everywhere?

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real analysis - How to find $lim_{hrightarrow 0}frac{sin(ha)}{h}$

How to find $\lim_{h\rightarrow 0}\frac{\sin(ha)}{h}$ without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...