133-Exam1BSolutions - Name Sou.) Tl ous Jan 29, 2008 Math...

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Unformatted text preview: Name Sou.) Tl ous Jan 29, 2008 Math 133 Q"! — First Hourly Exam Do all 5 problems (Total = 100 points). Show all work. Calculators are not allowed. (1) (30 points) Compute the following derivatives. d cos(a:2) __ .91.. u 'PNAU‘A‘ “Cl—‘5 “ J. q imam 1;:— “mm u=¢§=x"‘ dil- _ l "’1. «Jr: QAA x i 664 - '7‘ =1“ : 6. gr)? + )( d ' .4... 9“ 4’5an .1... A ' (blgglog2(\/81na:) = chi Q“ l l = a; (igmkgy‘ 1)) ._L .L , ' v .0 _ :' QMQ cl $M x C SX .— Co‘l’ ’X 82 QMQ (x—1>2<x+1 . , IL'(£E+3)2 ) TQ‘K; Qn ) ‘lZLe-vx Algcrefl‘lidjc (9049‘ SiJCS‘. (c) Differentiate y = On 1‘ ilflflhua) 3r ,QMU‘H} "JQ‘A’X " 1&(X4331 .LA .L 2 *_L._-‘___9;..] % 3%; = 3. l x4 x+l >< M3 (2) (20 points) Compute the following integrals. Make your substitutions clear. (a) /:2 1 dx. I uz’QMx a: lnx (le: x34 Sufi/ml - QuJi+C = New H. e,‘\ (1 => gxma _ QUESTL - 42:23 )2“ C. a: : 2(43-1 473 : QUE-0 (MAW/43”“ secztdt. . a. wk kl 52) an : £E+C = Elia 3h +C ,7 , halt WA L , mm) mm => Psmswa : is \5 ml?) - 5 .1. ‘ -° =2 t (3) (10 points) Let C be the part of the ellipse 11:2 + 4y2 = 4 that lies in the first quadrant. Sketch and write down an integral (with respect to m) that gives the arclength of C'. Be sure to include the limits of integration, but do not evaluate the integral. (0})- ' (av) Wk» 'x=o) «aiol am; bah» 7:0, «w‘s 2 =5 ‘Ivvleralc. 9c CW. 0 +0 :2. WW 2 l s Auger pay at = \+ may.) AM- 0 O 1 (4) (20 points) Let R be the region in the first quadrant between the curves y = —a:2 and 2 y = 4J5. Find the volume of the solid obtained by rotating R about the x-axis. iELSc Curves. Cwlmsccx’ (share, taxi: =5. X73347 % XH‘LLI‘X => ’x=o ex {5:01 sox=Ll ) .__.. —_9‘_ __._. shun .L X'Mix X: 0 'Lo X 3 Shop, a} ’X Lo q (pusher (JAE; We‘i‘us = 1— 1mm» who; \- = V; 50 Am mafia» :x(\L«-2§1 Ll \[O\W¢ : 3: 7t E; 0 I! 6: >1 h J: O "‘ L 6. \_/ Ii (5) (30 points) An oil tank is shaped like the bottom half of a sphere with radius 3 feet. If the tank contains oil 2 feet deep in the center, and if the oil weighs w lbs per cubic foot, find the work necessary to pump the oil in the tank up to the level of an exit pipe at the top of the tank. Express your answer in terms of w and 7r. La\H\ 3\\‘ce,s ‘38 t8 (JFK 7:0 a‘i EOHW 0.; $lx’cas Pawsg, 7:0 ‘0 3-2 1 (+0? 0% oil) Shae“ Ql hag/\i a :5 hat“ 3‘3 flu} flVY-iflfifn _ 3‘5 Aigk 0‘ qrck n Y1 = RXL32~ ...
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This note was uploaded on 05/12/2008 for the course MATH 133 taught by Professor Wei during the Spring '07 term at Michigan State University.

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133-Exam1BSolutions - Name Sou.) Tl ous Jan 29, 2008 Math...

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