test1 - \) Math 250A (Kennedy) - Exam 1 - Fall ’07 SHOW...

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Unformatted text preview: \) Math 250A (Kennedy) - Exam 1 - Fall ’07 SHOW YOUR WORK. Correct answers with no work Will get no credit. 1. (14 points total) Find the following /0 cos€d0 pan}: 7: 9 / v'= @19 M(9 ,/ V, 6 QSMQ -' J‘s.;8‘dg , 6.3.16 4— 0046‘ ‘f' C ‘5 d—di tsinh(t2)dt _2 - ICC/and Punlqmewfl‘al WQ‘M’“ ‘f Cad (“/“J r “L A ()7)? Sml‘ a J In“; .JLL f; gm. (Inc!) "4 ’7‘ D 2. (21 points) Find the following w dx m 2w (2+e“)3 /‘ 7‘ q ~ «2 = = ~i u H ~L : ‘7): {lie/k + C 77/2 /0 sin0c0860d6 fut, M9 “,9 Ultvfigg ‘ 7 v Ignace/949’ ’f “6 o’k :. -3101 1°C a $W15i~600169 J6 = ~ 1} 9:79 W“: a o 7 .L a —=% (w (2U win/77E 3’3 d - 2 y2+1y 5*; (4" 3 T/ M" 7’7 J? 2L {JM 3 favoi Ja ? M 3/; 1 '- i *’ UL~‘(1)‘[“: {(3501 —;uV 7‘6 3. (22 points) The slope field for the differential equation %% = g(a:) is : \ \\\\\ \ \ \ \ \ \ \ \ \ \ \ \\\\\\\\\\\\\\ / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / //////////////// ///////////// \\\\\ -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 (a) Sketch the two solutions that satisfy y(0) = 1 and y(0) = ‘—1 on the slope field. (b) Suppose y(ac) is a solution and c is an arbitrary constant. Which of the following is always a solution of the differential equation? y(m+c) No‘l‘ alwa a f“ “4"” y(x)+c I‘M-«Aw! 0 I” (“Am NOI‘ cult-v6.1.1 o. JoLWL‘D” y(-w) —y(m) fl(wa?1 u S°lbf|v°n (c) Sketch the graph of g(a:) on the axes below. 4. (12 points) Find the solution that passes through (0, —1) for the differential equation %=$51n(x2) 7' . {a L M 4 4: . Ju’ 24°C]? 9 5. (15 points) For the differential equation below, determine where the solu- (fimf(:\(°‘tjfil7' : P—(i/ 011A”) - #mx(k”/ +C tions are increasing, decreasing, concave up, concave down. da:_ t EU?“ is )0 2? (7° <21" j“ (,9 i? if." we” OIQ¢ ftf‘) “ ‘f 7’7"] F’- " z. (pg/‘1le G.(VG) )0 4:1" «4 <.+<! VW‘“ Comc ow" U~I’ Were If ~f’>/ if 7L<"// “(a Oohcaw «Law :2 {J5,;k JM ~£ “1/92 7‘C rec-l"? Mm {a (:C (a JCQI‘CGI ’6 Z c {‘7‘ .. ,_.____..__._. 6. (16 points) Define the function by It satisfies the differential equation dy_ dx- (a) Given that E(1) = 0.746824 ' - -, find 31(1) Where is the solution of the above differential equation that satisfies y(0) = 2. Jewel :6 New 5w 2‘ 2. 53(0) 50 big/ere ngcJ OTC 2— €(Q/TL. 5, 2‘7?(517 6"”2 f— —— $41») I l M £9 50212 N ‘7. ~ - K 9(0’: (b) Now suppose we want to find the solution of the differential equation and initial condition d ‘ y -— = = O m M) Find the value of this solution when a: = 1. 5‘0 (hf-1&- I" It ace—m , '3“) t; w (c) For the differential equation and initial condition given in part (b), express the solution in terms of the function .L L ~ '— ’ voxh)’a ...
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test1 - \) Math 250A (Kennedy) - Exam 1 - Fall ’07 SHOW...

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