133-Exam1ASolutions - Name 50 L uT\ 0 NS Jan 29, 2008 Math...

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Unformatted text preview: Name 50 L uT\ 0 NS Jan 29, 2008 Math 133 §l)'1 First Hourly Exam Do all 5 problems (Total = 100 points). Show all work. Calculators are not allowed. (1) (30 points) Compute the following derivatives. ' ' “ AM u l (34);; [efilnflj] -= %& €“2‘Ax :_ + C . x 'q i. ‘ ~ l“- midi.“ WM 4’ m = 9W «l i":'va:l\ri a )g f d ~ gl— QV‘ “*‘k EL XiQMll+¥llX (mg log2(m) - dd 2F.“ 1 a W l I - .1... . .4— 5 a ‘ 55ml hr 1" = x QMRUH‘) _12 1 (C) Differentiatey: 3 W Ema : KQQN‘U‘”) "‘ Q’V\(“*‘\ "9“«(X+3\ “" .QM Cesxk l _ \ ’ S’31‘4 §%:%lfij+;\ X+3 cosx ' “L 3. !(““\L(“') ~l—~ 3:3; '1— Q‘Dcv‘c] ‘2 3 Dev“) Lubx Xx-\+ (2) (20 points) Compute the following integrals. Make your substitutions clear. la) 3:0:iimdx' = = QM \+c \j u u “=34Si‘nx = ~I \ ' [du‘ 00536 (‘27: W L3¥$inx "gar a“ ’x) 5;; no oist vie valet 3:2)“ NJLALA > 1r4 x; u='\‘€\v~l£\ u\ “ (b)/O/ 3m” sec2tdt. Wig \d‘u2m‘L‘L d+_ “MA (Au — é. +Q h‘B we. have. ‘i 3‘1 3¥WG\$¢3l At = 2M3) 5 t ( " 3 O 5 6133 (3) (10 points) Let C be the part of the curve 312 2 1 — x3 that lies between x = 0 and m = 1. Write down an integral (with respect to 3:) that gives the arclength of C'. Be sure to include the limits of integration, but do not evaluate the integral. SJVL «gr 3 j a: (l—¥33i,1. ’Dlgdtcw‘hiuxe ‘ . 9M3 .19 as ’XL ,1 .— 3: 12(“75’3/ ' ('3¥‘\ = 3’7. ‘52:;- I \ Arch—fixgx = + A}; 3 S l* (:13) cl)! 0 C‘ (4) (20 points) Let R be the region bounded by the x—axis, the line ac = 1 and the curve y = 95‘. Find the volume of the solid obtained by rotating R about the y-axis. ,M 0,9) 1-“th ax gs 4m YA. 0,93. SLU— J. 3*“;3 3:0 40 3:0‘ Shea at; is a midw— 03+?“ Pagius (R 2 i Ivmcr ‘mJius ‘(' z ’X GoovA€na\-c. cf Fctv-A' on Curvc g=q¥fi (1+ Awe» 9‘ 8km '5 7': (RL‘ VL) \ = 7rL\—x‘3 - 7r(\—‘§F) 5cm $34 L5. fix “I _ -=I> Vflum=§x(\'%g\dg H >( K“ c wl’ wlr’ 05$ /\2 (5) (.30 points) A water tower consists of a spherical tank with diameter 10 feet. The bottom of the tank is 15 feet above ground level. If the tank is half full, find the work necessary to fill up the tank by pumping water from ground level (water weighs 62.4 lbs/ft3). Express your answer in terms of 7r and the number 62.4. LQLJ Slims a Ouyis \/:D alt QQAALA. cg leak. Slim-S W‘- e = 4v :5 l‘acli‘us “3 gm“ 7 O 5 C fimkjfif§¥ Slim, 03‘ ‘3 l3 disk. whose. radius ‘r' \‘s 36ft“ E3 ‘Hw Efimsereqnmmw‘. / Mm,» Sl‘iu, a} a is 20*6 get} (as Show) ‘3 wait ~. 3 mega .(m mtg) Ag 0 s = 4,23 8 Trv”.(20-+g\ '15 O ‘3’ .; 4,237: g (QB—ALBL105H63 A3. .59 L 3 = QQHW 3b 500*157'101 -7 5 ~ + g 7’- 19‘3 _. 15 t: (,2,Ll7'{ 3‘7 57 ‘1 \o = €2.47: (1500 + £311- 234?. 19MB /’—_—_—__’__________—__——————-———————‘ Km ...
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133-Exam1ASolutions - Name 50 L uT\ 0 NS Jan 29, 2008 Math...

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