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Math 1B - Fall 2007 - Zworski - Midterm2

# Math 1B - Fall 2007 - Zworski - Midterm2 - MATHlE MIDTERM...

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Unformatted text preview: MATHlE MIDTERM 2 {21111115111} Solve. earth problem on a separate sheet 111111'iti1u5 your 111111111 and section number on each sheet. Do 11:11: panic! Gnod lucid. Prohimn 1. {16 points} 11.] Determine Lht: r11diiofw111'er1mnce of the l'ullnwimz, 1.er pmwer series: L— 411:2 1'3,” 2— a : ZE_1) ”(TL-1]}: =ﬁlrn+i};T r-1=|'.| b) D11 the series in 1111.11. 11] cum-Hg? 11f. 1:11: 131-111! 11111-11th Provide 1:10.11: arguments I‘m” your 311.15%. Pruhlem 2. [E- ]nuiuts] 5111311111113. Ih11t the power 511an3 E 11,..L. ' cum-1111:5111 at r = E. What 311111.111: 11113 about its convergence at I .. —1':’ Problem 11. 1:8 pointﬂ] Pit-115113.13 the 1111111115111 int-35:11] 11:1 1111 inﬁnite merits: 1 1 .L a 3 I; (L — (ii) ) hint. linnmrkfIIiJ-Ita If 1.1311 use annualized hinmn'la! coefﬁcients, provide their deﬁnitinu. thiam 4 [E3 points} 1121 it"rite 11111. 11in: n—th 'Imrlur 11.011111211111111, ’1' [11) of IL: )1 111 :r. = D, b] Giw, 1111 estimate T111- Ii'n-LI}= Hm] - 3",.[1'] iur |.'1:|_ 11' 1.. a} Prm-‘e the EM 1111...tc for IEgILI} [f[3]='1'ul:;11} I- RDILILI). Problem 5. (12 points} 11] Find :‘1111 4th {11-1151'111-Tr11-‘lnr pr1|3.-'11n|r-.i.1] [mutt-1114.1] 111. ll] nf:l1<.- r11: 1.. T-J'G: I 112 EOE .15 . 11} Give a. nunmrical estimate for the remuiucinr va'ﬁd i11 |.'17! E l. Pruhlem [11:12 paints] .1_' Fj11dt1ue g1."1‘1011'11 sulutiun 1.11m following cliﬁmential mutation: VLF-I- 3:51—12. In; I'iml 1.'1u- «.1111 i111! salutinn nl' .'..'.-' .-.:.1.-11r= 61111111111 with time t:--111111'l="vl'.¥' 11:-1.c'.1I'l:111 11111.; . I'1_ Hal-1 _ I3) 2} yr — mus \$0353,- yn _ \$2 '13 '5" — i1 - If] 005:1: r n] Match the Fulkrwiug direction ﬁeldu with L‘l'lﬁ'crentiﬂl Equal inns (Planar: do uul. guess — points will be taken uﬂ’) 1?- If 3} y ‘1 _ .5 .aillltai.+4 a 1....rfrfii irilll IITGJJa/ _ “M . I. ..|.|_|.|-; . 5 . u . thIILIIIIIVFII+ITTTII - _aarxfxrx/ , _ 4 . wnﬂlFurt... tITilslllllllHHulll .Tilqulurrerr + bar LI. Ll I]... 15.an“..5 I.l I L llilnhriﬂaf .. xmwan} Elwin}? Kink-__.. 1...! LITIIJJJ/ 1w; xx. .IIIIIII till-73.1.. Il.l.1.|..ll...a.L. ..|-...1IIIIIJJ}I/ I Nu. m; iniiii m 1.16%} .4 Mil; n m .1 \...a....£.Ia H II..1I.....J.r';. ___\._\..x._ .I _P infaKMwL 4,... W131? wit.) we. ﬁrm». .33.. _:. .13wa urn-J \axﬁlﬁEHL... eriJIJJ/f .1._____ . xf/Iri? “Tu “ .......v.a..n.a .- Iqururraf HRH/.31.. uf. ill-ﬂiiuluallllul...“ .ll .I.1|:..Ii..tr. KNNKQEFIHIIIIIII F4 ..ﬁln.:.l...l.|-I1IIII.ILu.Lr.-In.. ...l...T!|._-.r.r....../ NW.“ ”ﬁrlilil ..-hnq-.l[rrrnuu-..=un. ”numMMNJ "Hg“ _unnnnnun h J. B 2 1 .L ._. J a... a. .___..___n Ernllﬂrﬁwuiz 1 ﬂ._.. ..2 1w 4. “_b _ . Jd ._ _ h. d. J. _ L.— J..z......x1,.,r... _ .____.__...\_..‘.1..”_1../...-...._..._ “5?. 3b.... 3?: _ 44/1. 3%.... 5/4.. :ﬂi EN... ._...,,....,....# 1 . . j ”unafw.ﬁjhxﬂ_ ﬁguqﬁ## 32:55,; __. 3.31.: m :33“ {a}... .36.»; 1.. n T33; 5.9.... “bar _wa«*¢ﬂMJ# kﬁﬂﬂ: __Exfﬂ “HHH1_,J ,u _LM/xa m. .33...” “__..xf/ ._ Jgnﬂﬂa w umwﬁvnyy. .. ___ __ g _, __. Lif. ##JLT i: . :1... E d. 3.2.1 B. 4.."1 am. a... aww. ...
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