Prove or disprove. The limit of a uniformly convergent sequence of polynomial is differentiable.
2026-04-22 07:12:14.1776841934
Uniformly convergent sequence of polynomial
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There are functions which are everywhere continuous and nowhere differentiable. Check the Weierstrass Function : http://en.wikipedia.org/wiki/Weierstrass_function
Then, in a closed interval, by a well-known theorem of Weierstrass you can approximate such a function uniformly by polynomials. However, the limit is nowhere differentiable.