2BsampleFinalSolutions

2BsampleFinalSolutions - A Last Name: Math ZB Final Exam...

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Unformatted text preview: A Last Name: Math ZB Final Exam Sample First Name: Last Name: Student ID #: : \ Section: I certifiz that this exam was taken by the person named and done without any form of assistance including books, notes, calculators and other people. Y our signature (For instructor use only!) Problem Score r Problem L Score 1 1 ’— 1’ 8 2 ” 9 ’l ”" 3 ”‘ 10 ‘l 4 fl 1 1 5 12 F" 6 L 13 '3 TOTAL J ID #: o This exam consists of 13 questions. # 1—7 are worth 10 pts each and # 8-13 are worth 5 pts each. 0 Read the directions for each problem carefully and answer all parts. 0 Please Show all work needed to arrive at your solutions. 0 Clearly indicate your final answer to each problem. 1.) 3.) Evaluate the following definite integral 3 [ (xZ—xmx 0 w b.) Evaluate the following limit €293 é (3.) Evaluate the following derivative d dx 8 f t2 etsin(t) cos(t) dt x 2.) Find the average value of the function g(x) = szv 1 + x3 on the interval [0,2] . ' (where f ' denotes the derivative of function f) with 3.) Consider continuous functions f and f values given by the following table: 7 6 4 qual subintervals. :2 v} sis , its; 5% fix w 5% 4% M J mi. , 1%.? we r k MM is the inverse of the differentiable function f given in the table. "aw We f (x) dx using a right~hand Reimann sum with 3 e a H; i in mu 4 a a Mr Mai Wk r]1 w? h x} r] C 2% H A. , 5 t 23:} rJO m , m. U 10 .1 a .m a V w m F E , S F MW; \../ “622$ \d b C a» 3 325 5:22 ciéééé kg m _ £22? / {icoyéfiéfiée ID #: 2 £2- and y=lxi. 3 2 4.) Find the area of the region bounded by the curves 3/ .fiEiEX ggsésgéifixfii ,2 WWW iéaé E w m 3 gm; 5.) Evaluate the following indefinite integral o v.1» 2 y“ 2 WM c, 9% I , a, z, .7 5% mix? mg? «iiiziyw , 4 w M 33%? 9 M4» Es gags; M ID #: g 6.) Find the volume of the solid obtained b curvesy= V4—x2 andyz 2-—x gfififiggfifiixfifigigeiézégééiz.._%.§:;§§ 7.) a.) Find a Cartesian equation for the curve given by the polar equation 1* = 35in 6 . 13.) Find a polar equation for the curve given by the Cartesian equation x + y :2 4 . tAa,Egg?x§é»§g,§s§é¥§§ {0 ¢ ID #: a: 3; 3% W Em {a :39 £22 w g i at . é§x§€ (we) a d dx 5% the following derivative “a a king‘s - % 2x E i go? g” E a 8.) Evaluate the following indefinite integral 9.) Evaluate. 3 {we 3! (Hint: Use x = sin y.) __ 1 1~x2 (Sin'lx) d dx l Q {Xe 10.) Use implicit differentiation to prove that / ll.) Evaluate the following indefinite integral [Sin35t dt ID #: rgent or divergent. Evaluate the integral if it M M m N w W 12.) Determine whether the following integral is eonve is convergent. %%%%%%wfi%§gfiflggggéfiéfigéeéigéézézzy9,22;a k w M weéw 5;; Km / (site: K V, {w Mg >515 2 ii 13.) Evaluate the following integral by making an appropriate trigonometric substitution if x2 W g” E ix “x , o. ,y g X , g m w m m ac,ng Mi o y Vi .m 13$ A , 2X siziiEéxw V a g 2 w g ,2; fiiéfiziifiésa. M M» ,H w 3 §§§fiywflw§fifl§$§§§§§é§5%,??55323i:32...?,_ ssss 3., a ,f . fig ...
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This note was uploaded on 12/07/2010 for the course MATH MATH 2B taught by Professor Famiglietti,c during the Fall '09 term at UC Irvine.

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2BsampleFinalSolutions - A Last Name: Math ZB Final Exam...

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