HW4-PA - £662: M421 HW 4 :32»; Due Friday Oct. 26 From...

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Unformatted text preview: £662: M421 HW 4 :32»; Due Friday Oct. 26 From Wade Section Page Number Problems 9.2 269-270 3(ab) 9.3 275—277 4, 5, 8 9.4 279 2, 3, 6 Non—book Exercises 1) For two sets A, B C R“ define dist(A, B) = M mg H5- 37“. xEA,yEB (a) Show that if E C R" is closed and K C R" is compact then EflK=(D, <2 dist(E,K) >0. (b) Find two closed sets E1 and E2 in R2 such that dist(E1, E2) = 0 but E1 0 E2 = (Z). 2) Suppose that E C R" is connected and E C A C E. Prove that A is connected. 3) Let f be defined on R2 by xlyla Z $2+y2‘ For which a > 0 is it true that lim 1:, =0. (aw—(0,0)“ y) jlxh’w‘x‘ 60 X? éé X’Lsfl ‘3 0‘] ":(Xl‘d‘ xii-11,1 X=€o a, 1‘13, [50/ [73/ 4 IXHM éZWV ['Fhmflijz— +-—-2 l 1— — ~ X1 (1") X H, X ‘1 cf (fl/O 30 v? [Mai/L Hum Wtle =) 313me 90 bd£ 2’ M52) MALL P“: “30% 2% ("whole Z "‘30 cop 2:90 :3 S“ is (low M £‘F5 M W [5 WM Q M+cod =3 3325c?) g» 2493} e [5 ml 4352.176 4:03) A w E: zmzwm AM 429443, (3} «V‘cE‘DZxJS: a we» mm W ~.-‘ .. g ..s 5 so X e 43 '{PA S‘mu) xra x; :3 {36:3sz a Cow}me “Yfl {1) L6} Alum“ blame?“ SM 406/ Mg W Couvpad T Ll} WMCMOW @ka AUfi J 2?th 0AA [Yeovewrb Q) 3 S'Mdkil 9k‘0toul ivy" VNA'S D'Lntt Como A Eva», ", Vnkwbg kink Cam {5 QA)‘ EV‘ ‘ “I i VVAwbq) Cow”) 4 U6' 1% ‘Y‘rw owe-mg AM?) W“ (Y 2 {V U 133 ‘13 cm 099% Cow/14,!" 5Q fiwwu§$3 so Ajv‘lv, v” JM n‘, q xm SQLWOgA gmq 2) EU. I "" ,VNIS 75 Q qucou, OM) @MM’DC: “6 AHA 43rd“ Now- book “:1 /—_—’—-. Fer A‘Bom‘“ MM Jas’erb): M Hi-‘W 726A 31:?) Skew “0" TR EC—Wj‘ is dove} cw.) K6“? 35 Coth -lL.M E was M M (EM >0. Mt. E Suppesn EMU—15 I 5km 4°00 +~ Jfi+(E.K)=d. Le+ ’yev. 'va. 8,4: =3 $693“ Wows OM} [3 (I, K I-Q o‘rsHE, K) :o +LM 3 iimg‘El ifiugc-k- [Nu—‘7» ‘ lln 9-96 :1 Nz>o 9 “213;” 2 1min +H°1L~§‘( _. 1‘72. + 32‘ ‘VlHZNg i E WZ- “07:22], :3 SEX—3'? Meow.) =3 ~ge—E => T: same 3H: Sim [W “I _ ~ g Swag E cl?“ racomeoloel ad E c A c5 . P‘mw 9‘5 A 75 Comm“ A 15 Va“‘ COMM—e544), 3 LLV 0M ~1- UnAi¢ UUVDA V M 496 WW 2% M EcAcUflv 3% an“ (U35 535$ via \A/Lobv UNE, MayeeV/M =3§eE 53333;ch 4% “xiv—333 m 6V 33-3 rm «aw Erma) $<3 §MEE =9 3:14 0‘) )fi’wfliw 6 R743? #‘ N Om, 'book W——/ 1:3 L2} -\‘- ‘01 0L9:in w 11L1\ito.o\‘5 \gq M“ ¥(X( 2 L/ a W ¥or w\m\A «>0 Is Hr erz “d 8““ ‘Q (X011 :0 X—éo L S \Xvul I; ,A + Mi“ 4 élX‘lles+f‘l‘1’ M Fm 230 m) L) l\§\‘¢5 5‘ l 5 L i S ham 5%1X1\X\5+%lw\lvl - P 5 m + 65 M i £55 (1&4le WM (,2 hwflpk) § IXM“ < CESUX‘IKHMQ) Lcé—S L ‘ __/ ~ X “1“ X1 p11 "5 ww- 2) a i X LA} 5-- I X17!“ )4 E Y'ML "" X M“ ‘9 564;,“ :6 °< (1:4 040(I-l LH‘ Y3K) 6w) X—-)o N1” I u-l *°° M4“: L 1 M :3 7: 7H0“ 1x1 (“‘2 Conn,“ [11 we )‘W QM) =éo £40 ...
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HW4-PA - £662: M421 HW 4 :32»; Due Friday Oct. 26 From...

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