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Exam 1 Solutions

# Exam 1 Solutions - MAT 2020-003 EXAM E Name K 95:‘4/20 1...

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Unformatted text preview: MAT 2020-003 EXAM E Name K 95 :‘4/20 1 0 John Peter Score / E00 Directions: Show all work carefully. Minimal to no credit will be givenfor answers without appropriatejusl‘lﬁcalion. 1. (10 points each) Evaluate each ofthe following integrals: 1 com/f j l q: (h) f 253sz ~i— MK i Leif} afﬁx? r'? ge} €§ﬁla+z {la Over-9 2. (10 points) Sketch the region bounded by the given curves. Then ﬁnd the area of the region > ‘3 ﬂag? w (“’é’“ “r A (3“) a. («— a) If = 5.; {3) w ,. 3- (12 pﬂints) Find the voiume of the solid obtained by iotating the region bounded by y m x/E 3 3’ m 0 7 X =6, andx = 3 abouttheliney m —1, 1,383? x g {x} a: "i? {a%§'i\f~ HOE? 4. (10 points) A force of 30 Newtons is required to hotd a spring that has been stretched from its natural length of 10 cm to a length of 15 em. How much work is done in stretching the spring from 15 em to 20 cm? (aim: 4? (tee) ~== 30 “‘ a g5} : Rafﬁ§ 39;, (>535: Eeex tie-aka: \$608?) :: “ﬁx . t AC: X2 gm “£2?” 2-: 3ee<tei~teeztﬂ =3ésﬂem>>ezzz§ 5. (16 poiilts each) Evaluate each of the following integrals: (21) I; 259“de a: X xi: afﬁx Ciuz&ws (N: 69% 53“ t a. t - m vi nge &>< =2: - xe XL} “*jff \$1; m w + <~e“*\:“> (b)fexsinxdx a. x ,_ 5. h t {As—6. \f.» “’{223C 2:- g‘smx_ g'ex5mK81Xs : 36 ,ﬁVISEeX \$1M X é“ '6 &X 3%; {g}? “'6 £93K +€X33ﬂx “gﬁxﬁsnxé‘xh 6. {10 points) Evaluate f sin2(ﬁx)coss(nx)dx “5: § :32me wgéém {issﬁﬁﬁcﬁx H x n l S Sinzfﬁﬁ 5% S§§Ifﬁx§ {Les {W§)§Y 1.6“ {it ggniwx‘) ialuﬁ misﬁﬁcix : i" gazO—wualﬁu 3 x ~4xmlo 7. (1.4 poin£s) Write out a partial fraction decomposition for the raiional expression m S x3~4xw10 Hum—d Then evaluate ihe foliowing integrai: f4 x2_x~6 x 2 X i” i r ,- - V g :3 z an X K {a E Xgéﬁﬁgn 4x i9 xgﬁéxd‘nw m ) 3XW4 by: ._ ,4 0,57% 1 w XH + . » xz+ 1’2 it mm x “ "X “"{é (“agkg -» x2 - x A <2; 3% ~43 j \$3; i gxw 4 m A + g b \ p m ‘2. mam) m2. KFB W: X M ,§_ M. A. W x&z KWE 5 2x“ ‘4; ‘1‘; Aéxﬂi-g it gbﬁ’ﬁ _ S 1 ° 3 , ‘ 2. t 3 “3‘ "ﬁ ‘3: (‘ﬁ‘ﬁ'QY “3%”??? _ Wgﬁc 3: 3:— .Hi 4r Zﬁniwﬁ «ELﬁaé‘t-ﬁé 3 3:“: AJka ' v. 4 “:2 ’ g Q g 23”?) 3%; 6 , 23d ‘3 £3 a 33 “‘" :WSM‘ZE @«a ~4m»%(g~g§ +13% “75% ’E E? + (a h “'45 :- 5'8 "q ﬁ 7; H "i; ’- <g+ é a» 232m {éﬂ Bonus (4 FREE points) True or Faise: This set is é Wﬁéﬁmi '3": *?fﬁ€%~% ﬁaéz§wZ§arzi ...
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Exam 1 Solutions - MAT 2020-003 EXAM E Name K 95:‘4/20 1...

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