exam3bsol - Math 16B (Fall 2009) Kouba . Exam 3 KEY Please...

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Unformatted text preview: Math 16B (Fall 2009) 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. . Make sure that you have 6 pages, including the cover page. . Include units on answers where units are appropriate. You will be graded on proper use of integral and derivative notation. You have until 4:00 pm. sharp to finish the exam. capong . You may use the following trig identities : a.) sin2 0 + cos2 0 :1 b.) 1+ tan2 0 = sec2 9 c.) sin 20 = 28in6cos0 d.) cos 29 = cos2 0 — sin2 6 = 2 cos2 0 — l = 1 - 2sin2 0 2 h . ‘ .. . .. ' .L ' z I < __ __ ‘ II 10 Absolute E1101 for Trapezmd ml Rule 1s IE, | u (b a)12{ 021:?be , h4 Absolute Error for Simpson’s Rule is : lEnl S (b — a)~1§6{ magi) [f(4)(;r)|} . 1.) (9 pts. each) Use partial fractions for each indefinite integral. ' a: 3 _, _ FL .13., a')/x2_:_2d‘” ' §W%‘§Lx»g +x+11JV (ALK'FQ‘F Géxvaz] : X+ 3 X+l : :23): (XvélI‘fg’fl’WiX‘f'f/4’C/ L / $2 ~VX+I v L ween—xwyafkwe+mkx (Awe/2+ @Mwfi: ><Z+x Jim/B“. “8=(—* 33‘! mxlmyé m M ~. 24+67Q2+W®j=5~92ACQ 2’) =M%+%+%flex : «Mixl +31<_+ aM(><—z]+c film W 4W 2.) (9 pts.) Compute $6, the Simpson Estimate using n = 6, for 11:2 + 1) dx . -3 *2 —( O ‘l R 3 _ ‘ Wk i’l : b q 1‘. g 6 57 :; I 2 ‘4 2 e 54: .35.. [#63)+q%x)+ a 462+ 42%;; a¥0}+q£(;y+~F@3 I: igpm zo+¢1flxn5+ Mn &+‘/%I + afloat—A Yflgfl—Am} (,V 6.75 3.) (9 pts. each) Determine the value of each improper integral. 4.) (9 pts.) Use /\/u2 :!:a2 (111. = (1/2)(u\/’ua2 iaz i azlnlu+ Vuz‘icfl) + C to integrate / \/ $2 —6ac dos. .SVx’LLoxJ-x :SV®£@x+7}~fi . (MM:X~3——>A~a:d‘x2 a:3) H 1 du=lln 5.) (9 pts.) Use / u<a+bu> a (HINT : Start with a u-substitution.) __L (Muzfl/vtx—a om- X M) Latex 4:3/(024/ :LM( "‘ (+C u a+bu . 1 +0 to Integrate / W dm. 5W” 6.) (9 pts. each) Determine the following indefinite integrals. a.) /(tan2m+seca:) dIB :: j I + M —-5 : ,sz J. V 3 L ’1 b)/a;(lnz‘)2 d3: avg/L 0’2 X x Q‘K : Mamet: MMW {www OWN? a A w —- J. V : LXR . ‘ A ' >< / A = ZXAQMX/ —— g—xl/Mx » :‘ijx 47C] - L 4 ’2 t .z 4 \ 01K @435)» 524(1qu +75% +C, “Jr—a c.) / em cosm day (HINT : Use integration by parts twice withxa twist.) :CX‘ (mu:c/ aVscaqxéLy XMX~ C—wax—f‘ggx cam”? : fixwx + 95 wx— Sex wxM QWW A K +42, a M26X4¢< V: ‘dodxj = Q ——>, RSQXQOQXij—‘v/ €XMK+C WVC‘FC’a é QKMK‘F‘i'E/XWX + C/ Sixaodx Jde t 7.) (10 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 = 1n (1 + isf”(;r)=m22(::i)2. /lln(1+%) dz]: (a; : Twl. lsxsoz (SKSA X‘Qmj" ' Q)*a+/)& *1/ l 9x - . G 5‘ _ 5' r Wit"? 7”} is? ’/ 1 A 1 5— 7/; 5’ V‘ 2 (Hy/@0005] “5 Q” r 3 (@576; 0005]) EXTRA CREDIT PROBLEM~ The following problem is worth 10 points. This problem isOPTIONAL. - 10/ 1 d6 __ S l , (~M6 GIG 1+sin6 " (+M9 (~Am9 : g L._.._)‘M5‘ 49 -.- g ————‘K“MQ ow vmke 0/0430 Q l __ Me #1 Slur? me (:04 ale : SCwexmeme/oee : Warm/06 C/ ...
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exam3bsol - Math 16B (Fall 2009) Kouba . Exam 3 KEY Please...

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