exam3sol - # Math 16B (Winter 2008) Kouba Exam 3 KEY Please...

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Unformatted text preview: # Math 16B (Winter 2008) Kouba Exam 3 KEY Please PRINT your name here : _________________________________________________________ __ Your Exam ID Number __________ __ 1. PLEASE DO NOT TURN THIS PAGE UNTIL TOLD TO DO SO. 2. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO, IN ANY WAY, ASSIST ANOTHER PERSON IN THE COMPLETION OF THIS EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO TAKE AN EXAM FOR ANOTHER PERSON. PLEASE KEEP YOUR OWN WORK COVERED UP AS MUCH AS POSSIBLE DURING THE EXAM SO THAT OTHERS WILL NOT BE TEMPTED OR DISTRACTED. THANK YOU FOR YOUR COOPERATION. 3. No notes, books, or classmates may be used as resources for this exam. YOU MAY USE A CALCULATOR ON THIS EXAM. 4. Read directions to each problem carefully. Show all work for full credit. In most cases, a correct answer with no supporting work will receive little or no credit. What you write down and how you write it are the most important means of your getting a good score on this exam. Neatness and organization are also important. 5. Make sure that you have 5 pages, including the cover page. 6. Include units on answers where units are appropriate. 7. You will be graded on proper use of integral and derivative notation. 8. You have until 8:50 am. sharp to finish the exam. 9. You may use the following trig identities : a.) sin2 6 + cos2 6 = 1 b.) 1+ tan2 6 = 8602 6 c.) sin 26 = 2 sin 6 cos 6 (1.) cos 26 = cos2 6 —— sin2 6 = 2 cos2 6 — 1 == 1 — 2 sin2 6 h2 10. Absolute Error for Trapezoidal Rule is : lEnl S (b — a)—— max if’ 12 agasgb 1.) (8 pts. each) Consider the region bounded by the graphs of y = fl, y = 0, and gr 2 4. Determine the volume of the solid formed by revolving this region about (SET UP INTEGRALS ONLY) Val: «— 3:017) 1M a.) the X—axis. b.) the y—axis. Vyl : T8:C4)23;7 ~— TF §:()'2/2J;L 2.) -s 4" v .— ¥ — 5 [ll (8 pts. each) Determine the following indefinite integrals. a.) /(lna:)2 dac / —I .. M..X 0L1) V_.X xéMX/i—Zl—X/QW~ 3‘ dwjzxanxj’; qxfinx+o2x+c b.) /(1+tanx)2 dac : SO~LQM><+7CM¢3~XJ 00* ngx+ ((+MRX//o% 3QMX+ szf'kr 2 2M(mxz+7€a4x+c, 60/511990 d9? tffl/‘VVLXU‘WQX2Jfi/ SCMX~ Mx MOZX) M’ ~m><~ SMX m‘xw (wwwxg I (Lu ~MXM-A“0LM:MXW MX v*3vv‘atu : ~co<Lx+ 337M3+¢ ~M>< +—3‘—me)3+¢ a .- A .- —q 5‘1 : 1%},[41L024- q-FQ/+2~l‘—(g) +4 +(3jwt—41ea] ( _L. 1 Elf—[(+46 +£(2; +<lél§2+é253 x ((37 4.) (9 pts. each) Determine the value of eafil improper integral. A a. 00; a: " _l—' :M f“ )/12\/3d ’Aeoo 31alf><~éfi A900 X ll :MC—M—W):m—l:o© 4—500 3 1 a 8‘3]~2 b)/0 (9P3? dm — [4%3— o “my _. 144/4 — _ "‘ A _ M :L __ SJ") ’ Aaa‘ (X 3) l" ,A—VB” 4—3 3 ““l H J. _ 00 .1..- = “‘1‘ ~ 3‘ ‘ _ 3 ‘ 00 5.) (7 pts.) Use / V U2 i a2 du = (1/2)(ux/ u2 i a2 :l: a21n|u + V to2 i a2l) to integrate the following : Want : 31/rx*.<ox+fi)~cr av 13m M CM”:X'§ M: M2433) :_ fiCCxwh/ba’)’: 33L ~ 32flmlé<"3]+'VQ<”3fi'3al)+c 6.) (9 pts. each) Use partial fractions for each indefinite integral. :v+3 __ X+3 _ A 8 r (ALX+I]+8L><~;<): ><+3——» xza: 3A=5~aA=ifsj MX="I‘ ~395=<1 —-> 6: G7) 5/3 ~"2/3) _ Elam _ 1,, C :S[Y5§ ><+IlJ7' 3 [X &/+3MIXHI+ x2 Xl-Ful A A b)/x3__+2:2dx __ S Kafka) 6%: [X +XR+~———X’9\ 4% (AXQ<~01]4 86<—a/+C><*: xii—(:2 A MX:01~;8:2—»8:—() Mmz: gaze—s Cicyqt‘B/a/ I _ MXHZ “A~C~/]+C3/,2): 3a-A1é—3/k: "’/ :1- 3 - .1- .3. _ :5[_§>+ X4+2§i]4y:gflmlxl+x+Q/QM(X 4+6, 8.) (8 pts.) What should n be in order that the Trapezoidal Rule estimate the exact value of the following definite integral with absolute error at most 0.0005 ? See the Error 1 Formula on the front of this exam. Assume that the second derivative of f = ln (1+ —) _ ,, 293+1 3” 13 f (x) : w2(a:+ 1)2 ' 2 ,1. _ ’ l - J. ,/ /11n(1+%) d3; 2 (+x (/\" M " V\ i -I_ A I we I I ,9 EXTRA CREDIT PROBLEM— The following problem is worth 10 points. This problem is OPTIONAL. Wmlmdx (M “mt—w, i, ‘4/ I AM: figDH—I/ 97 X _ >< I K M SX‘z ><"+I #7 V 5”?” s ~ ' A, L] 1 30442642) M ‘ [M—( + “+1 “(M CALu+1j+€Lu~ljzl ———5 MM: &/4=/——?4:1/;¢J 102+ r1 76=z—~ 13:79») I ~/ Hf: +6. KM ...
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This note was uploaded on 03/14/2010 for the course PSYCHOLOGY 556666 taught by Professor Gill during the Spring '09 term at Abraham Baldwin Agricultural College.

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exam3sol - # Math 16B (Winter 2008) Kouba Exam 3 KEY Please...

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