1021 Final A Term 2007 answers

1021 Final A Term 2007 answers - MA 1021 A ’07...

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Unformatted text preview: MA 1021 A ’07 Instructions This test is closed book. Calculators are not allowed. Part I - Basic Skills Final Exa II 5 A01 Heinricher, A (PLC) A04 Wasyk, R (8:00) A07 Hrynkiv, V (1 :00) A10 Tang, D (10:00) A13 Tang, D (12:00) Please Circle your Section A02 Abraham,J (3:00) A05 Blais, M (9:00) A08 Malone, J. J. (1:00) A1 I Masamune, J (2:00) A03 Hill, M (8:00) A06 Burgos, C (9:00) A09 Tashjian, G (1000) A12 Hrynkiv, V (3:00) 1. 2. 3. aFmd——ny= 5. 6. 7. Part I — Basic Skills Work the following problems and write your answers in the space provided. Use the scratch paper provided for your work. You need not simplify your answers. No partial credit will be given for these problems. t 3 5' fl.“ 32.x '3‘ —-~ Findgif y=7+2\/;+3x4—§. Ans. W + #1“ x _ —“_—*— Find i): if y=x5tanx. dx Find 3% if y=esi"x. Ans, e; {3053K dy x3 ca 2—5x' 1%»7 Findgif'y=h1(x2~—7x+18). Ans. Xlflxflg “Hle Ans. 711' ~5- £31“ . . 2 3 Fund — If x + =0. a J’y Find an equation for the tangent line to the curve y z x2 + 5x — 4 at the point (3, 20). Ans. y "-2- X “" E3 Part 11 Work all of the following problems. Show your work in the space provided. You need not simplify your answers, but remember that on this part of the exam your work and your explanations are graded, not just the final answers 8. Evaluate each limit or show it does not exist. (6 points for each part) Vx+2—3 a. lim x—>7 g; ism ><+am3 ) {M2 +3 r [EM 5:?” a raw and. Ux-ra-a 3 we": (xm1(®1+3) '3 iEM Km”? K %%7 (K47)(VPW .3 low fl: M26) WW War} (a . tanzx b Mn x—->0 x ‘3' it“ 331% .... itm (Sz‘nX>( ssh s “were as Cofilfié' Keg a 595%; a: lam smc wax] a) a M o x wee—mam... "2:: .——-. i O 9. For f (x) = 2x2 + 7 , find f'(x) by using the limit definition ofthe derivative. (12 points) 10. A boat is sailing directly north from an island at 20 mph. A second boat is sailing directly east from the same island at 25 mph. At this moment, the first boat is 40 miles north of the island, and two boats are 50 miles apart from each other . How fast is the distance between the two boats changing at this moment? (15 points) ll. lflé‘éflfwi In this problem, you will analyze the curve given by f (x) = 3x4 — 4x3 (This problem is worth 20 points) 21. Find all intervals where f (x) is increasing ‘ijgfi “:3? [2 ngm 12%;. Mg; =1 in? (“x-m 1) are/ha! gem-lg - x20) xtl $5,519?» eke a... bag 5—1 ties + {mgreagivlj 6m 0,-5’06) b. Find all intervals where f (x) is decreasing @ecrwwj on (“09,ej W (a) a) c. Find all intervals Where f (x) is concave up way «a. 15¢ka Mg 251‘ Concave U? {33" (“092% W (16,09 (1. Find all intervals where f (x) is concave down meN/e 65W” OW (0)273) 6. Find all local maxima and minima of f (x) $129 :4? mail Keen! exma; 5mm gagho‘m éeemfia’fv [M W (13%,! 7g: 1 z“) [ogn/ Minimum, Since fiflffiwm Jifffé’fiflg {fig} W Mfrweal‘mj fléM [film éfic’mge 7C'T—f 70MB fin (zér/LOQ) bah-gait (“j (a;me Mi? 3 f. Find any inflection points of f (x) Iflg'leafiaw Path-l Q x7210 .SthCQ. 1%; ELM-v Lia/rwmfiw Ckflvvije} St 54 WW9 ) M alga a)? X277"; (1%! {—an We mama g. Sketch a graph of III-IEIEIIIIllfi lilli=l=llllll IIII-IlZ-£$IIIIIIII III-Illlumllllllllo II... . III-I...- 12. Find the maximum possible volume of a cylindrical can if its total surface area (including the top and the bottom) must be equal to 540%. Note that the area of a circle is m2, and the area of the side of a cylindrical can is 27rrh, where r is the base radius and h is the height of the can. (16 points) Zfir‘z-«h ZWFL’X': Vt; Erik. r: NE a“ egg—FF“ <5: Wefla‘fiue «bl/"a?" 9AM flgymmain; $0 la: 270—61: [So _ 60 r 3076 w?) tho; r: ;m fifmed? V=1Tr‘\n: W(3fiof% 1 Swan 1L) \ch (Mcfiea £5 concave five-M“ / 13. 9m J. ‘3 0‘3“. Find the derivative of the foiiowing filnctions. (6 points for each part) a. f(x) = sin5 (x2) : ‘+ _ a; gSln COS (Xi) —.—.- 10% M (x1) w (2*) b. f (x) = 3cm” (05X 3 x ,, J2“ (xwfl :— (Cosxfl’lm 4% Xx '; @5‘1’“){QM¥)+ (MEX) 0.98% ;< ’— ', ){CDSX ((—usfinx>(/qu§)+ (M 14. Use linear approximation to find an approximate value for V3 128 “ (J3poims) ‘— / \ 3 4:60 : XVB Ff (x): 3 X my} g; 128‘ nD/(a)=-— i429 ) A _ ‘9 r,\ 1 “L. H 3 L‘H g 1—02?) -=— _ 3 _ + H g 5” “:— 5.0% 3VL<5 m A Calm; (4353!; US'njr afar»: §. 03% WL} ****** Endofexam ****** ...
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This note was uploaded on 10/13/2009 for the course MA 1021 taught by Professor Tashjian during the Spring '08 term at WPI.

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1021 Final A Term 2007 answers - MA 1021 A ’07...

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