hw1 - (c For every > 0 there exists a δ such that | x...

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M421 HW 1 Due Friday Sept. 7 From Wade Section Page Number Problems 5.1 114-115 2b (note P n given in 2a), 3, 4, 5, 6 Non-book Exercises 1) Complete the proof of Remark 5.7. Show that if f : [ a,b ] m→ R is bounded, and P,Q ∈ P [ a,b ] satisfy Q P then U ( f,Q ) U ( f,P ). 2) Negate the following statements: (a) It rains every wednesday. (b) If wednesday is rainy then the following thursday is snowy.
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Unformatted text preview: (c) For every ǫ > 0 there exists a δ such that | x − y | < δ implies | f ( x ) − f ( y ) | < ǫ. (d) sup x ∈ [ a,b ] f ( x ) < ∞ . (e) f is Riemann integrable, that is: ∀ ǫ > 0 there exists P ∈ P [ a,b ] such that U ( f,P ) − L ( f,P ) < ǫ. 1...
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This note was uploaded on 07/25/2008 for the course MATH 421 taught by Professor Promislow during the Fall '07 term at Michigan State University.

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