Math 31B midterm1 solution

Math 31B midterm1 solution - 1. Evaluate the following...

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Unformatted text preview: 1. Evaluate the following integrals: ! 2 1': sin; : _ a.'[11}1—xd.r b. In c. Intanlxdrv 1. I —l . - ‘If-‘h 9'. Mt A’M’W. 71“” {F'flxvfik : fur/Mist :f-lL-lfij'f i " --r r f : E: Mfzi'f; [E r 52 “It. A, Le?’ Mr W- 2. Evaluate these integrals. [Don't forget the constant.) 1 = 7 1' mm a‘ {buggy 3 Egli '{MMjf 5 75401;): ___, fulfil}: f‘fmfii “T “'35-— : v __ {-sz +flrlrgoxf +6 If 3- 3. Consider the curve given by the equation y - f(1)- '3 + e- For anya :0, find the length ofthe Curve from x 2-0 to .r n a. [Note that the quantity you get under the square root sign simplifies conveniently] Show that your answer Is equal to f’La). J: EX; ‘3? 1-!- 2 ' y: 0 : :Léifi; 2 , 548—»: f 2 (a /’A’ 4. Show which of the following improper integrals diverge and which converge. 1f convergent, evaluate it. a. fIJDOXc'd-I b. c £2“{1-x)dx M -mby J i -' . #4 #395714} Jr“- 4:{ x WJ’MW —-,m’ .‘ L. 0:1,. I! {Minx x '1 M f“); £45; * Marv max fig Mwm/%%g)aav LWE#J aggflwiwx I 1 If f If C' [ E—VJ'W/v = ELEM?!» iifm/‘J 5‘ I -06 I .. - I , : -' Jr at l. '4‘. 5% e fer/w em I“, 8 I” . :gflmémé” awmfl%r - lV—pop .-d/ 5. Use Simpson’s rule to approximate the following integral with N=4z [3:3 + 2x + aux. Then find an N sufficiently large so that the ermr bound 515;) will be less than 10" __ ,4; _, a ‘ #. Ant-‘45 gfjr2.[fir¥%a% *:-7::-;’H J 5:3 : m) g: :2) g r" 7/; fi Wer HM +537 'b:m.'%/rj -“-' 3;“: 211?}; ‘ V9 “W ‘4‘” h M Ma Far Hi: (“Y/W“ afifi'mfléé 55. 5.1L; 5” MWN 53742;" M: Q Mi gal mol/ jg. mafia/7’5,ng— ‘— am; g 5352, +3 a‘Tg—g ...
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This note was uploaded on 04/06/2012 for the course MATH 31B taught by Professor Valdimarsson during the Fall '08 term at UCLA.

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Math 31B midterm1 solution - 1. Evaluate the following...

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