exam4A_soln - Your Name Printed Clearly Your Discussion...

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Unformatted text preview: Your Name Printed Clearly! Your Discussion Leader Name __—_______ Discussion Period EXAM 4A 0 BOYLAND o CALCULUS 2 0 FALL 09 I”, we, 1. (a) {6 points) Using the product of two series, find the first jam nonzero terms of the Maclaurin series of = 6”” sin(.r). i , '12, \3 ‘ . ‘3 $5 bofk st/mx ;{/+><+/:,+_>_<,+...>v<xa% +2: +rt> COM/78 6 t I (goraHY 2— 3 ‘7‘ 3 H :><+>‘+§L+l€.+ +~_z,__>:+.~ .2 é é 6 (b) (4 points) Use your result from part (a) to compute lirngflzflv—m : _._ ‘ 2 3 v _ / Y‘QO X2, : “MA ‘ +— : i 360 “:3 Page 1 of 5 Total points this page out of 10 2. Consider the curve given by the parametric equations m = et —— t, y = 46t/2, 0 g t S 1. (a) (4 points) Write down the integral which gives the surface area when this curve is rotated about the sis—axis. t A% _ t/L <31. zeal, —-— a 36 ch. 6" —-—-—---1 fit/2f 4t 1 1; 1 SAINT 3 “limit” *‘Qe (b) ( 6 points) Evaluate your integral from part (a). Lt t ‘ + Li. .6 I Q 9/7. VL- Lé’jle +36/ “‘fl 3 Page 2 of 5 Total points this page out of 10 3. (a) { 5 points) Eliminate the parameter to find the Cartesian equation of the curve given by m=1+1n(t+1),y=(t—2)2+3. x: ffM/¥fl>/ x—(: h«/gfi%'€$4:f+( (b) ( 5 points) Find the equation of the tangent line to the curve given in part (a) when the parameter 1% = 0. 4% : {t'l $1 :“J* g“ 2 >’ one %+/ v ($1: _ / 0 A / .——’———- 75-0 CM :9 it” Page 3 of 5 Total points this page out of 10 4. (a) (4 points) Sketch the curve given in polar coordinates by r = 4 (305(30). ‘61; ‘36“. r ’g‘ f 7.“ x 6 TV a? m? E 5 E (b) ( 6 points ) Find the area inside one loop of the curve given in part (a). “76 .2 At, TO’ML 24R“ @O’F 0" P L5 TNlK “\5 (’00 :Q' ’1“ gm, 0 cosgelL°L6 2. 0 TV: Ae’ ,- 2 .. ,,L a (99 g“IL Cos Bag/6 ~ 3d lL 2i] + C 5 1 O ‘- a TV Oar-O-‘O 3‘1}!— f 5;.4 éO a 1 ,v—v. : file T10 4 5 ,4 at. Page 4 of 5 Total points this page out of 10 5. Consider the two curves given in polar coordinates, r = 3003(6) and r = 1 + 005(0). (a) (3 points) Sketch these curves on the same axis. r : 5 £05 6 3 r: 3 5056 V 211' "P[ r: 11-6056 f r: 1+cob6 (b) (1 point) At which point(s) do the curves intersect? _ l “ COS 5 a /2—— / o I.“ _. , 6A6: 3 , 3 SW Hiwcoslel ‘ 96‘” So 3”“1‘9 W9 0 TVs ___d If If d5 3 6 '1, 5 .. flew/51% L W 95E? Page 5 of 5 Total points this page out of 10 ...
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This note was uploaded on 05/21/2011 for the course MAC 2312 taught by Professor Bonner during the Fall '08 term at University of Florida.

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exam4A_soln - Your Name Printed Clearly Your Discussion...

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