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Sonika posted an Question
September 17, 2020 • 17:45 pm 30 points
  • CSIR NET
  • Mathematical Sciences

What does tbis thoerem represent ??? what it wants to say

Tences (Real Ar al Analysis Cal SCen Tences Theorem : Let [a, b] be a closed and bounded interval and for each n e N, let f, be differentiable on a, b]. If each f, be continuous on [a, b] and the series of functions f, + f2+ f, t.. converges uniformly on [a, b] to a function g and the series f, + f, + f, + .. converges to s on [a, b], then s'(x) = g(x) for all x e [a, b]. 9PR 3 la Proof : Let s x) = f(x) + f.(x) + + f (x)

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  • Sonika Jain

    can u write the exact meaning of theorem little clearly

  • Sonika Jain

    what exactly this theorem is saying . like what are the conditions that are required and what is concusion then ?

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    Satpal singh best-answer

    the above theorem is saying about the uniform convergence of series of function by the help of uniformly convergent series of f' (derivatives) bcoz sometimes derivatives are easy rather than given function . so if the series of derivatives is uniformly converges then series of f also unifirmly converges.

    eduncle-logo-app

    here are so many f fn g s all are taken can you please elaborate

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