Exam4Solutions - Name Sour; ! Digs April 15, 2008 Math 133...

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Unformatted text preview: Name Sour; ! Digs April 15, 2008 Math 133 — Hourly Exam 4, Do all problems (Total = 100 points). Show all work. (1) (30 points) Determine if the following positive series converge. Justify your answers, making clear in each case which test you are using. n V F _t_q <a>S=Z “1 Male, Algal av- < = hm Ml. 712+ i *3’7- CDth ( ‘?-$-er‘§v¢s . n (b)S= 2n+lnn 2 70‘“ 13% am “b Wm M r = x Q ‘ a \VW\ “.35., 1 h n . y Rx, h-fioo 5“ lye?” an-ylbm,‘ “L 2 --:-————- .L 3'3. lQM Gm” , QMWMAI M a 2'y(m(“+\) 0X hfiw an h‘M’Q m*“‘. LIA-h" “4°” M M ' 9% ‘ Y‘L (2) (10 points) Determine if the series below is absolutely convergent, conditionally convergent, or divergent. Justify your answer and make clear which test(s) you use. n! S = Z(—1)"W m . . n n‘. n‘. {EST 'Par QB»\UL¢ COM/«3mm; Ni)“; an = ‘6‘) @“31 \ : "" GKVQ', have. \lm‘ 3: WM“ .Can‘)\. but u -> 90 an QCHHT“ n \- : hm comb”? (Mg. ha» sum . and .(fi, - M J— ‘ .1... .. '7‘ gig; 2n+\ O f. S Convemacs O'OSoluLKB ‘36 TEST. (3) (12 points) Find the interval of convergence for the power series below. Do not test for convergence at the endpoints. f ‘9 5 I f H “M W n-w ma. I‘2>X~7.\ 13 lm \3x'll“ “*' h->°o “*1 .. ._ \ l ‘1: ‘ l3¥ -2.\ (HM “40¢ 2 \3val. ."8 _\T\¢ (AkrVaA a‘ COfiwatnCL {A all “Y wl‘k 13x'1\<\ (in?) 4m. RA». Tm} ‘ ‘i‘ms is -\ < 3x'2 < \ l<3x<3 §<x<\ W 0 Hi, .p (4) (12 points) Find the Maclaurin series for the function below. Express your answer in the form Zanx”. You are free to use the well-known series for sine 07" cosine. cos(a:2)_ 1 L! a m — C°s«=\-?‘-.:+l‘—.-%+H ' 2R¢P‘3CLX 38' ‘1 8 ’ i Cosxl=i"%+~x7-%T+Z%:_n Divas. (tack Afar/rah X Y n - CDSXL_J--l:+i_§_+}£: ‘ x .L‘. '1' Q! 3: “" \ X I l . . - ._ " K. W . A ~\ Trné (LC‘UZ!“6 \5m‘A’ OR a * Z"? x n ‘ Madavn‘a Series Laces)»; n;\ Lavq‘. cg Hus {lg-51%» +erm , »f\ bvwio. does QUINthac m (5) (11 points) Find the Maclaurin series for the function below. Express your answer in the form Zens”. You are free to use any of the well-known series that you learned. 1 Z "7(\)3 Wis Cl £;V‘m\‘& Series. €1VOMCVA 4M>3 = \ + HAL—fl 1- (-3354) My o} L~B\(;i?('5) (Ms ,e (swanky-LL); ‘f.’ =\»%x+ Britta-L513 346%. 4+ 2‘ 'X. 3! -\\ L“ X .. W. L 5.‘ \ .. if _._. _, 3 . i 3* * 2'1! X J' 3.6‘. ’x “ 1 fi‘ XH 4—" 00 (h \ .3— +1). P\ __ (n+1\(mr\\ .VA or 9.01!) x - a. x ' n10 n=b Q9 Y - ,l ‘\ u-v \ ' $6¢o-\c\ i"\€\'koA mf‘iex “"543. 3 [v 3 E x“ V 60 . QAA Ai‘qercmL‘A—f— “\ufim ‘2 M (V. KY?— = i “ xvv‘ // (“>93 “ABRFVf‘H-s win” V\= M V.-"5 ‘4 W‘L m AiR-crcutkdti. a \p : RLM"\% L x “A:l «v/ N (6) (12 points) Find the degree 2 Taylor Polynomial P2(:r) of f(a:) = 6/5 about a = 8. Write the coefficients as fractions (not decimals). (7) (a) (5 points) Rewrite the polar equation 7‘2 = 4?“ sin 0 in Cartesian coordinates. mea XLX1L=TL and 3=rsb~9 1 "Hats \‘3 s '7. eowac saw M . z 03—- 1\ + x = ‘1‘ gfeey \‘S Cit-ell. Z Cevvkr L0) 13 Wins 2 , (b) (9 points) A particle moves in the plane along the path given parametrically by :r(t) = 400515, y(t) = 2sint, 0 g t _<_ 7r. Identify the particle’s path by finding a Cartesian equation for it. Graph the Cartesian equation. Indicate the portion of the graph traced by the particle and include an arrow showing the direction of motion. x" L Tc+t=l Emgsc "Pdr\fo\¢, Wm 65 COVAA'H‘CAOJLW {5e. 4%.,“ 3103,3th : (Hp) is (m, ‘6an : Hp) ...
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Exam4Solutions - Name Sour; ! Digs April 15, 2008 Math 133...

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