mid2_sol - Problem 1. [20 points] Diflbruutimv Hm...

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Unformatted text preview: Problem 1. [20 points] Diflbruutimv Hm function. in] [5 points] ft.r) =(t05(.~iill(t.ml.r)) f7“ = -Sm(§m&ow70) ~ Cospcawfl - Secz x _ __ | l _'/ 1W _4’I l p4; 2P4; I P4- "” [5 Paints] fir) = silfltuum ‘ 1111:) v _ 1 Jr £9» ) ('(x) = 191n(,+amx-!~X3 Cos (’Eanw .430 $9; YRMX XJ ’L ‘M's ( r+ 2' F}; M [5 points] j'Lr) : (‘1 _L‘,..’\um. r 3:0 +11)“ X x. [M3 2 {any flmflix‘) - - \ P ' 2v 2 9+5 :0— ; Seng“(H)<l)*JCW‘1‘-\‘;:Z ‘0 IJZX’UW‘) ~~-Z|o4S. ?’(X3:‘ (\+'12)Jmmx(§ecz)< ’oflfic‘fkk3 ‘4. XL “‘3' [5 Points] 1"“ = ¢ _‘=. QM‘RY‘K 2: Mutts) +-‘:—0M(v—+~+H T LAX-H) 4 1 L044) 1‘00 ' 2W3) KN zoom we “’27 3 4 3. v + 3. Problem 2. [10 points] Find dy/dm. (a) [5 points] ms(my) = :ntany 5‘“ (“‘33 (43+ “$3 2 Jam“; +9L $e83 ifi—‘g . \ d_ {'xs‘muvfl —')L$'Pc?'~; : funtg - ‘3th (n3) 4% {'MV)*V§SYM(K*3) __'—-——‘— f—‘p— - “ 7(SUACXL3)» 398:)» (b) [5 points] (13 + 1):! : (yz + 1);- lg kHz—MW”- 1 9,4614 0 - -— - \ p-h m .4 %L(i‘+0+ '3‘ f; : ,QMhSz-(O-Jr 7t ‘02:“ X 2W 2W} cl‘é : ( 743 ,,_.i__. (@034le ‘33“ '3'; 1’“ 3 '1“ 21% C“; )thm ’ x‘u - AV 5 Jmh‘ktm _ 27:2} ZP-‘s 2v+s w 1P4) Problem 3. [10 paints] 'l‘wn curs. start moving from the same point. Om- tmvels north at 30 mi/h and the other [mu-ls ms! at .m mi/ln. At. what rate is the distance between the ears increasing after one. hour later? k=3or 3'40! ?=£;O 0‘ l clr,}:_'i::i£'—‘—°_ 6W“: 3:44 t" 9° g Problem 4. [10 points] Estimate can(().0()1) using a linear approximation. L94 ‘FCxU: tam/L Tbuz \Ineaw awwx :4 {an ad 0 is {CH a: {Van (X—o) 4 (0:3 ‘ “ ‘ ‘5 10‘“ {Wmtsec'lY ~—~- 7' P)" {'(n: '1 Ho): 0 {:00 it V ‘- 7’ [7+5 Thu/s Problem 5. [10 points] Find the uhsulutc minimum and the absolute maximum of the following function: .c“—6;r2—151'+25 fox-US$56. 3 'L Lei {00 = X '61 “W”? 3“ 3x1 \'l\o('l\~ table-*QY'S) :3(x_§'3LX—f\) 2 Fig x - .- CVHVJ Vuflmes '. a, g. ’ o \ a ' gimm ”\ is n“\ 'IV‘ domain ’ bu? m7 CVKKLM 1 2 4 fig: 53455 49:12:? a P5 L-7§11§ 2‘79: ‘ '3 GMAPD'HA'\$ . H°\:rz'§ R0: 634-345-439? I t -—°\o-* L? t j Problem 6. [20 points] Let f(:1:) = 1:3 —3:1:2 -—9m+6. (a) [7 points] Find where f is increasing and where f is decreasing. (h) [7 points] Find where f is concave upward and where f is concave downward. Find the inflection minus). (c) [6 points] Using the information from parts (a) and (b). sketch the graph of f. v- ’\’ (“7 Rx”: 312'!" "°i = 3CX1'2Y ~33 :“s(x-3')Cx+t7 t P I " ( ‘7. 9%) IX X (-i ’ {0‘770 =1 mweur’vw‘ ‘ 1 V“ xx «(5((3 _ fl,n<° g; d-QCVCQSIWg * 7-4 x73 {’60 >0 '3) THCWO‘STV‘Q ' ' ' ' 1 i7 5 h . \ + O9) 9’? KW t 6X—6 :6( Y-O p .e . . 7. 5 I? s<<k ‘ ("(x) (0 =3 CohCAi/E (\omvxwowds '94 Leis -~ - '7- (A) ”C,<) >0 .2) Commvo Uffibua 1+ ><>L , H 2P“) infler‘l'iov PAM . Qi—Fm} Z ((I'Y') (0 «Com: —i ~3+°\*6= “ {1-9: 33-2._21—¢1.7,+6 = -27-¢L’-'1| (,\ JViS. Problem 7. [10 points] Show that .r > sinm‘ for 0 < .r < 7r/2. L01 €50: 1-3'MX €’cm=t— Cosx --"‘ °> {7+5 Ix’ o<v<l{, 4mm +(033 0 “ ’ ‘ 7' P+5 gfhm £00 TS 171010157713 ob (o. (ham; ==‘> Tncveou'uwg 3946 Problem 8. [10 points] Find the limit. (a) [5 points] lim 111(1 + 3:) 1—4) mm: (h) [5 points] JW firm a; .L x x900 9 '2, ‘7‘}5 '2 [945. ...
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This note was uploaded on 02/07/2012 for the course MATH 1271 taught by Professor Ming during the Fall '08 term at Minnesota.

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