Wednesday, 6 March 2013

real analysis - When can a sum and integral be interchanged?

Let's say I have 0n=0fn(x)dx with fn(x) being continuous functions. When can interchange the integral and summation? Is fn(x)0 for all x and for all n sufficient? How about when fn(x) converges absolutely? If so why?

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real analysis - How to find limhrightarrow0fracsin(ha)h

How to find lim without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...