Michigan State University Sequences of Functions Questions

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Mathematics

Michigan State University

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these questions all based on theorem and definition. doesnot need plenty of time to do it.

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Problem 6 Let ______ and _____ be sequences of bounded functions on ICR that converge uniformly

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n=1 Problem 6 het nyo and of guyo be sequences of bounded funcbons I CR that converge uniformly f and g. Prove that fut gr, fn-gn, and fregn also converge uniformly. on т to ♡ Problem fn: IR R. be ne N V het Ini I (0,to) sequences of functions that uniformly converge Prove that as ho. disprove Problem 8 E n h n= het f() = 3 cos (nx), f is differentiable the interval CE[0, 2u] Prove that on ท [0, 20] Problem 9 5 Prove that Ź tan a mi) n=1 [ informly [- [ ] um on ท Converges 第く Problem 10 sW an x Consider Ž (con (2n)! n=o series Converse on xan sum noo Prove that the pointwise R and denote the f(x) S (1)" (24)!!! Without computing f explicitely, show that f twice differential and f"=-f. IS
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Really useful study material!

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