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# hw1 - (c For every Ç> 0 there exists a Î´ 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 ] mapsto→ 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 Ç« > 0 there exists a Î´ such that | x âˆ’ y | < Î´ implies | f ( x ) âˆ’ f ( y ) | < Ç«. (d) sup x âˆˆ [ a,b ] f ( x ) < âˆž . (e) f is Riemann integrable, that is: âˆ€ Ç« > 0 there exists P âˆˆ P [ a,b ] such that U ( f,P ) âˆ’ L ( f,P ) < Ç«. 1...
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