Can we show that $$(\exists \epsilon \in[0,x])\left(\int_{0}^x \frac{(x-s)^n f^{(n+1)}(s)}{n!}ds= \frac{x^{n+1}f^{(n+1)}( \epsilon)}{k!}\right)\text{ ?}$$
Thanks in advance!
2026-04-04 00:19:02.1775261942
Can one obtaining a mean value form of the Taylor series remainder using the integral remainder?
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