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Exam2_Solutions - MAC 2281 004-— EXAM 2 Name QLWLJ...

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Unformatted text preview: MAC 2281 004 -— EXAM 2 Name: _ QLWLJ “T“IQN E: The exam is worth a total of 150 pts + 20 pts bonus 2 170 points. Calculators are not permitted. (mex-I-l)2 (3 x“ 1)3 , {(22 mail Ci’éw 63 w (x2 :x—HU [(5x~1)3] (1) (15 pts. ) Differentiate y —~ 2. (qu X“) (x Wm?) (ixﬁ) m ,wa W ”WM an... )MVW‘V I w M“ mmﬂe MW w WW A «ﬁx a 2. e a 9 (x ”3:; 3,73 (ng b 0 (3w) WC 3%: 0;}3’W3‘9 I WM , (x ”x+») f? (6x_3§§j!2ww33:;iwm;wmew ‘ em“ I Cxwx1r13;<‘2>‘"‘®i‘32 CW 3: W WWW (éxi-vULt W 6‘? ”(3 Mg}: w .Simplify your answer. (2) (15 pts. ) Differentéate y = sin2 (3x) cos2 (5x). \$53: [Sm (ﬁxﬂ . (9.)“ )4.) 5+ lggihz (39x3 \{QU : MY 3:: Q g‘ﬁg “23%) [)\ﬁ( “\$53K ‘ ﬁgs (43“!) “3%" ~43\f°\ 1(333' .23 fﬂﬁ<€ilﬁk3 [:6 930%” ”:31; cinfbx‘) wsCBx)- BX) ca§£5§x3+ sin? (Ex) 2 003(5).) C 51x16: x3) (\$5 %’ 2:. 2: (5 5x m 5X35 gm ”“ .2 SmC‘pr) CDE)(3:)><) 3 ms. (5X) .2” 3‘“ (3” “m C 3 3’ L _w ”W” ,m «4 4W”... M- a» MMv/wwwwm .4159» r...”— [ a“ w: 2 Smtgx) 69;;(5x3- if) ﬁ;°>(3 73 mlgﬁ) w 5 343%) axnCESX)1 15.....w-W W/rﬁﬂa-.. ” (3) (15 pts.) Differentiate y = (sec(x))x «01(3) :2 :6“ Wan?) 2917(3) 2:. X: £ﬂ<\$€a<>®> bi‘gpawan’{ﬂ\§1 L108 EM} akcjﬂa with Feﬁf‘wgc jg) x 2 we: 3 ang: :2: ’( «QﬁCMCCxDD rag» >4: [IQpCs amixﬁl (235 im CngéaCxDD + X ML»: (56600); a 53:2:er I ”L. 5mg: . {:0an3 82:. 8 (26h (Seek?) v“? X {09(9) [5L CSecCXDDQ («CDCgeCCxDD 1r X EamCxD>\ y/__ #6., ”.4”:me .w-w «W (4) (15 pts.) Let f(x)— —— sin 1(\/_). Find f’g). £I<JN W wwmww‘j‘ “W“ WW“; Wit)” (5) (15 pts.) Find an equation of the tangent line to the curve x3 -- 49:31 + y3 = 1 at the point (1,2). Digerm§c3£§mg me‘kiﬂg wan (“ESE—Ci; 1:33 K , we: 29%; 3X2? Ly-(xay + 332%! :2: Q 5X22: 4-(1-5 22x-a’)2+ ”552:1; :22 0 3X2)” 4%} “" 4X3] £122: E23823! 2:0 Pct: (42,2): 3-1912 12—222~F}~21-3’+5222.‘a’:© “1‘: {mi Llf‘xé}, REA iﬁuaﬁon 0g; "Una: ATM?) (am :2“) T: :92» (94 ’13 22? F6 22’ w 2% 2:2 5?; (6) (15 pts.) Find an equation of the tangent line to the curve 6"” +x + 1 = y atthe point (0 2). <2 t; :1 x mg Qt D1\$¥er“an”¥1ajc}n3 \MF\\Cl+I\a' um’dm Vﬁmﬁ-JC “k: g I 5%: (>418)! +— 4 1» O a La glove: Q? My; {:anaeméi; Line: {:3 m 113 _ (7E quajwﬁ QC {3119 111111115101 {21111 (a 21:): 3 (X 0) 3:) 6213/1 :E) M WWWX 11:3:3; l. mum! m.» alyﬁkwmﬁmll . Jr A .. a-.';-= .(. . . ~ mum-a (7)' (20 pts.) The position function of a particle is given by s = t3 -~ 9t2 + 151:, where t is measured in seconds and s in feet. (a) Find the total distance traveled during the first 7 seconds. (b) When is the particle speeding up? When is it slowing down? (00 g ,3 6 g QEﬂde‘E-l: :2 l;- (elm CitWWi’S) v: e’ a ”seam ico‘EWle‘S’m s—(eﬁ ems) zs-CeMD-Ltwe) I W WW sf?) :2. ‘1?» . (“elm (ll-"iii: anti) W ‘f- (’qu W 63445 ) anord game} Forwarcl W l} 1 ch Kim—J 59(1) ‘W 5( O) T“ :31 . Fl 0M '11 3”» Q {to Alix-17W", Far Such MQWQS «Vortxaﬁsrc; if” *9: 33(5) W 5(l5 2:, ”~13 VI} :1ng . iii-ram {33‘ "to {1“ng Parke?» (“wees \rﬂCLmarﬁ QEJQ; 36%) M 5LE§> :3 "give—'25): ‘3’)“. ghost“ {3:63 JR) L39“; PMBCAQ moves ePDFuXN“Q\ 31‘9: ' . ‘e ..,..m\c_ JCS‘avejec; duﬁn We, 3“ch i} seggnde ‘3‘ ”Mummies, 7:34ch Cheek” ,e. 8 £ 7,..+“32;+~‘152v2\3’i 4,th dam 3.5.9.4 W (is) aev’e {semis asleep OcrzO Carl‘s; L3 3‘3- » mg . McWAsw-ys £4 7 y . _. y“ __., r ##3#me why-“+37 . LWWKSJLM w”. W6 \ Slow‘in , Speedivg. Sevnméci U? (known elation (8) (20 pts.) A man starts walking north at 2 ft/s from a point P. At the same time, a woman starts walking west at 4 ft/s from a point 20 ft east of P. At what rate is the distance between the people changing after 3 seconds? Is the distance increasing or decreasing at that time? X fblS‘CC—lﬁcﬁ ‘ backweﬁﬁ “one! Lumen and (F a: Digjgpxnca [thei'kmezef’i “Jane. man 0AA F. :1:?: % :Elg‘cancg be‘kcoaerx JCJ’Q» VFOEAQW égw Life . '2. 7 “:1: X M . V-W yam- rkrmwrwm ﬁt \62 r “a; ,>< . A, Kleenex-e43 a: ' “W? AlcyOn Jaime: decreﬁnﬁocgf \Sa Jamel, ”LIE" “*1 w“ Li” ‘Q‘JL/Ss. 7g l5 \6 {'3 lﬁCc'Qoﬁ/Sﬁﬁgb Ba JEEMQ— 35%;:3 Q» PKML/S. in % mmmﬁ/ meom walks 4-3341?{ 30) x'mZQMlDN32¥£. ,. .OOCAS (W00 WQ‘LS 2 E) 2.7;; g “ELL” 31:), :1 g ¥{:' in 3 sec / Ne "cl/ml: Elma) “22?“: \$1 + (31:261i-«r336 MOO. 530/ 2.2:lQ ft. " 321» ll: HQWQ. 4:1 ma ‘ (9) (20 pts.) A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 2 ft/s, how fast is the angle between the top of the ladder and the wall changing when the bottom of the ladder is 8 ft from the wall. Xirblb’bance, "cl: ”Hoe Bottom a]: ﬂag laclaar gm ea mu. 8’7 An le logboaeeﬁ Dee, “be? 0&1 Una, laid, ma tie mu. ﬂﬁwﬂw ”ﬁg; 5 l h 9 :1 Maia“ t: ”fl—(3W . X 3“ W W a: 0339' WE We are X 15 incveaemg baa lame, giw 2:: g gig/5 \ \ \ J" {'3 HA W ﬁtscaeaf"; aLGELb lee. Una heialqje t)? {\m; (LAB? g :9 é) a 2" a. W, ‘13:? A (9?" V ‘QOW git. 733%: \$53,, ‘52:: . \Xﬂneh xii?) Q43 ) a W W 0 W \ém M 5:: Ht 3: Ne ”Unﬁt MW”; We “ ”’15)" ~ lb 5» (10) BONUS (20 pts.) Find equations of all lines passing through the point (03) and tangent to the curve at2 + 2y2 2 6. Let: (0919) be: on Fotnt: 0m ttwé; Curr-veg. >34 Axis; é; rtjne, rtﬁtngf‘ﬁrt: ting; Faggagx‘ ttxrrauata (0,3), wk are, ...
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