hw1PA - £062}? M421 HW 1 i Due Friday Sept. 8 From Wade...

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Unformatted text preview: £062}? M421 HW 1 i Due Friday Sept. 8 From Wade Section Page Number Problems 5.1 114—115 2b (note Pn given in 2a), 3, 4, 5, 6 Non-book Exercises 1) Complete the proof of Remark 5.7. Show that if f : [(1,1)] H R is bounded, and HQ 6 ’P[a,b] satisfy Q Q P then U(f,Q) S U(f, P). 2) Negate the following statements: (a) It rains every wednesday. (b) If it rains on wednesday then it will snow on thursday. (c) For every 6 > 0 there exists a 6 such that lx—yl < 6 implies | f (:13) — f (y)| < e. (d) sup f(av) < oo. mE[a.,b] (e) f is Riemann integrable, that is: V6 > 0 there exists P E 73[a, b] such that < 6' 501*5 w: 3 ~ I C) X X E c z ‘./rz [we prom .ijf (:E: E: EU\\3\ E ‘m mxwab om cow mg :5 m 1&9.an Ema“) Pix {701 Col/\S‘x’vu(+ ? é Wflmfl ‘3» 'u(£\p)-- LH‘MAE, “[57” 1’ +20, Wg'qil- “4%” \ . 0g ' ‘15 ‘Q , /N l Lefi Nu ; V2 w 237;” Leg} Priaggu it: 212)} V) <J- iQ‘gIéLpllzlzr-J/V}. 1L!” L H3330 Shun M: =0 on Mmkmfi L. x, .) “W M“Q ~ ’ “fly w" ‘w’ :1 ' o om w; "flmflfij/ n 2 \; ‘iku-Q M U MW) 2 “WM-13-04: a + N-I- Zfi a. 320 5 32 WNW) “Hffl £58 :3 fits NMW 45mg 3‘}? an : gm 3 Sup QSQPO Pe@ Q )0 W Q0 Wybl‘é’row .— ._.( C3 *9 woe» +ka+ 5; Gum) gm «Mr 6" SC {Hawk to V C. éDqu :H {MM :10 V Xe Dub] ‘1": reodté VXEUI‘OA 90”“); <¥v¢vw +142 («OWP‘M‘é‘M Prmdyfie, FE WW kw 51m:va 4k} T‘c c, e- Can} Owl Hume] MW “3:02.03 n 3: £853 b c. b SECXW '~ Saiméx +L‘90dc9x New AS$uu 4W0) 2‘0 £07 Son? Xoecvsbjj XBYJ X0“; 30 9;ch 2S Mac» :0 Q a BTW 43°13; = sww 3:“ an? 5 swwsk Mir way 2;ch e: Law. Tab 5 So «WM Hm} Yrcwflf’ om (ace-5, 2w?) 500 Shae ~F i5 Cok‘h“ (4005} X0, ‘l’k\\5 P059} wLo‘r ‘9 (K0) >0 9 ...
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hw1PA - £062}? M421 HW 1 i Due Friday Sept. 8 From Wade...

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