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history-page42 - | f k(x | ≤ M k on[a,b for k = 1 2 3 and...

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The Weierstrass Approximation Theorem: If f is continuous on [a,b] , then there is a sequence of polynomials that converges uniformly to f on [a,b] . The Weierstrass M -test: If
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Unformatted text preview: | f k (x) | ≤ M k on [a,b] for k = 1 , 2 , 3 ,... , and ∞ s k = 1 M k con-verges, then ∞ s k = 1 f k (x) converges uniformly on [a,b] ....
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