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September 17, 2020 12:15 pm 30 pts
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 ?
• Satpal singh
see this
• Satpal singh
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 eas...