1021 Final A Term 2006 answers

1021 Final A Term 2006 answers - MA 1021 A ’06 Final Exam...

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Unformatted text preview: MA 1021 A ’06 Final Exam Name Instructions This test is closed book. Calculators are not allowed. \ Part I - Basic Skills A01 Heinricher, A G3LC) A04 Tashjian, G (8:00) A07 Masamune, J (1 :00) A10 Abraham, J (10:00) A13 Tashjian, G (12:00) Please Circle your Section A02 de Oliveira, G (3:00) A03 Servatius, B (8:00) A05 Onofrei, D (9:00) A06 Fehribach, J (9:00) A08 de Oliveira, G (3:00) A09 Malone, J. J. (10:00) All Lui, R (2:00) A12 Masamune, J (3:00) A14 Abraham, J (11:00) 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. d 4 1. Find—y 'fy:x3 +3x2——3+5 dx x l2. d 2. Find—J: ify=x3lnx dx dy (x2+1) 3. F' d — 'f = I“ a1 y e (em 4. Find an equation for the tangent line to the 4 . curve y = x — x3 at the pomt (1,0) Ans. z: x‘l dy 3+x 5. Find — if y = 2 I dx l+x (DU-+1.1)" (3+X)(7->0 «W Ans. ll'l'x‘f“ d 11 6. Find—yify=(x3—3x2+5) I dx 0 u (xv-nus) (ht-ex) Ans. d 7. Find l ify = sin3 (x) dx 3 Slh1(¥) ((05.3!) Ans. Part II ‘ 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. . x2—9 a.mn7;———— x+3x-+x—12 __ 1m (x+3)(x-3) _ I"... “'3 ! >973 (“fits—3") i “73 7"” .. lm “'9‘ _ ng 136933 3+3 4. —— —. ' lim X + [trim If 7 X93 . ‘16-‘93 .'5wa+25 b. 11m— x—)0 x .. hm ('5'- x+2§ )(H H2? llm 257(54'25) 2-90 x 5+ may ’9") "(5+\/¥+15') : llm Fl x—eo Sh/x-t-zs‘ —-\ ——. .4 __ 9M _ lo ":5 him .._.I 54*0 .— __________,_.______..———— —-- “m 5+ ‘ ’lhm 6 him 9.. For f (x) = x2 - 5x , find f'(x) by using the limit definition of derivative. Hm.) Mgr/fl [um 97%) '5 kfio k Dcfimhe» 0“ a. d‘flV‘A hut, Iv \\ p 7‘ + (7 I \r\ \l N x l V] 10. Find an equation for the tangent line to the curve x 2 + xy + y2 = 19 at the point (2, 3) x l 7 v4.9 :1 .z .— if... dx may 11. A ladder 13 feet long that was leaning against a vertical wall begins to slip. Its top slides down the wall while its bottom moves along the ground at a constant speed of 3 ft/s. How fast is the top of the ladder moving when it is 5 feet above the ground? 1: i6“? 1: (7‘ l‘5 iflCfflU‘ljB (1‘1 "x Q at m1 01" if; t (-‘2‘ :: HZ‘: pi'/5l'c‘¢: [5 éecr‘i‘T‘SEfi) \/ team ’5 j 11, A LTERNATWE 5 fat—U TtoN A ladder 13 feet long that was leaning against a vertical wall begins to slip. Its top slides down the wall While its bottom moves along the ground at a constant speed of 3 ft/s. How fast is the top of the ladder moving when it is 5 feet above the ground? 12. In this problem, you will analyze the curve given by f(x)= ~x3+3x2 -oo< x < +00 Mt (“MU—*2) E “6:0 x=2_ a. Find all intervals where f(x) is increasing F’H‘; -.= - 3X (“306*4) M (Home) (+1 (-) — '2. (b. 7-) m (-7 t In .Lnln\ z..\ (-g-\ .— LL’ 1 W \ J k I 'WX) liner-ease; 6n (017-) b. Find all intervals where f(x) is decreasing FCK) dlfleak’; 6n (n 00,5) M (2) you) c. Find all intervals where f(x) is concave up Wm: -— (Mr -: emu—n ~=> W I WM) 0 p’fit) 4. 0 6.00) l) C‘fl‘”) l5 Concave up on @0030 (1. Find all intervals Where f (x) is concave down in?!) [S Concave clown on (Iii—db) e. Find all local maxima and minima of f (x) crih'catl pomi‘y 1K": 0 Md W137— 4" fiéow’) W3 1:0 15 ad'th Gab, l), a. festbn “Au-L [5 [onto‘we up -' flu jedcfl'l Mll/Afiéejcjé I“; a, Inca] Mlnlmdm. (0,0 1, +0“), 4» N55”. wlmm . is (max-r9 down-r b7 flu Seamd dean/15c 7435i; 70-; Z 15 a, [on] maximum. (2, LI) f. Find any inflection points of f (x) 0m possible Fatiml '7 when: FII/k):0 9 x r: I FY!) I} (onhnuo'r fin at neighborhood amt/I‘d x3!) and (Wat) is POSIM/c +0 “4: fer”! Jf Y7]! “6‘91”: l 1117 HM r5,th of X61; 'hau; Xv! 1'! am lflFbcM/l poi-44' (1,90 Sketch a graph of f (x) III... .- IIIHH-II III-I-l I. III”...- Ill-II.- I' III II.- UI‘. E...- % f_ i- I _ no» - II I IIIIIIII M II. I III. III- nw-I m III I III-III- @ (0,5) - III I Ill-{III- 7 (HI-‘1") ,/ “ t 1,4/ 13. An open top rectangular box with a square base is to built with wooden sides, and a metal bottom. It will have a volume of 125 cubic inches. Metal costs six cents per square inch, while wood costs two cents per square inch. Find the dimensions of the box which will minimize the cost of materials for the box. ‘2 . 3 ' Volume-r. V‘J )5 l, ., l'Zf In Casi-:67; éxl'l- 2(ley) I 1:. l1; >< x 9} x1 1 175 __ 2 Moo c602. éx + B’x(.;;), éx + O4 X < +00 C/{X‘5-5 11x“ loco 31.14:; Zena MW) )9“ [2x7 [600 F x“: I20 [7/ WV $ecgnd dmvafxirc (.5 pojtfiw X ._: 19' 4%! x [h AOMfiIhI' he?!“ cont‘ve {/71 Id {fig . cdmfpemd; fb 4L fitobal mmmwm “ft 3'0 1‘5 14. Find the derivative of the following functions a. f(x)=ex+xe+(e)(x) P/xk— €¥+ 6769-44“ 6 b. f(x):xsinx In y =, in xsmx“; (S'hxiflh x) L 4.2. .. (cmaww @‘M‘Cii ‘/ d)‘ - anX 4:1 —; [(6% mam + 11"]7i A): >‘ c. f(x) = sin(esx) Man—— [Cos (8‘)] E e”) [if ****** End Ofexam- ****** ...
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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 2006 answers - MA 1021 A ’06 Final Exam...

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