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# FUND CONCEPTS ANLYS MATH 424

UW
GPA 3.76

John Palmieri

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COURSE
PROF.
John Palmieri
TYPE
Study Guide
PAGES
1
WORDS
KARMA
50 ?

## Popular in Mathematics (M)

This 1 page Study Guide was uploaded by Addison Beer on Wednesday September 9, 2015. The Study Guide belongs to MATH 424 at University of Washington taught by John Palmieri in Fall. Since its upload, it has received 32 views. For similar materials see /class/192070/math-424-university-of-washington in Mathematics (M) at University of Washington.

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Date Created: 09/09/15
Mathematics 424B574B Autumn 2007 Study problems for the final There Will be some problems on the nal Which are based on some of these there Will also be some problems on the nal Which are not based on any of these H i Exercises 36 3 12 318 E0 Let an be a sequence of real numbers let p7 be a sequence of positive integers and let 7 mm P2a2 A A A Pnan P1P2AAAPn Prove that if the sequence an converges to some number a then 127 converges to a also Cn 9 Let 220 an be a series For each n let 3 a0 i i i an Let 127 be a sequencer Suppose that i the sequence snbn1 converges and ii the series 220 3 12 7 bn1 converges Prove that the series 220 anbn converges Theorem 3 41 might be help ful Use this to give another proof of Theorem 34 and also use it to solve exercise 38 H i Exercise 4 4 2 Given a function f z X A Y prove that f is continuous if and only if Q for every subset E of Xi 9 Suppose that f z X A Y is continuous Prove that if X is compact then fX is compact Prove that if X is connected then is connected Only assume the de nition of compactness and the characterization of continuity in terms of preimages of open sets being open Can you do it With just the 56 de nition of continuity F Suppose that f z X A R and g z X A R are continuous De ne h z X A R by hz minfzgzi Must h be continuous 01 i Is there a continuous function f 01 U 1 2 A R With f17 0 and fl 3 Is there a uniformly continuous function like this

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