hw1 - (c) For every > 0 there exists a such that...

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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 > 0 there exists a such that | x y | < implies | f ( x ) f ( y ) | < . (d) sup x [ a,b ] f ( x ) < . (e) f is Riemann integrable, that is: > 0 there exists P P [ a,b ] such that U ( f,P ) L ( f,P ) < . 1...
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