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ex1sol-a - MTH 133 m Section 5-8 —— Test One DEPARTMENT...

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Unformatted text preview: MTH 133 m Section 5-8 —— Test One DEPARTMENT OF MATHEMATICS Michigan State University September 20, 2005 NAME: gfi it”??? ID NUMBER: SIGNATURE: SECTION: 1. This exam has 5 pages including this cover. There are 8 questions. 2. Include units in your answers whenever appropriate. 3. You may NOT use your calculator. 4. Sines, cosines, and tangents of simple angles are to be written out. For example, if you have a (305%), you should write 3?. 5. Present your solutions to each problem in a clear and orderly fashion. Include enough steps7 including diagrams, to permit the grader to follow your method. Your method must justify your answer . PROBLEM POINTS SCORE 1 10 2 20 3 15 4 10 5 10 6 10 7 10 8 15 TOTAL 100 Present your solutions clearly. 2 1. (10 points) Find the derivative of f (3}) = sin (111(1 + 952)) “ q a , , 2’17" 4" f ’ L. ‘ ~ ’5 ’3 z ) , A $62 5%: 3% i i? >< 3 M: H/ >4 2. (20 points) Find each of the following indefinite integrals. (a) / seczxeta‘m’dm l% > *afi :><' :jkéfidjw éQMSEFCZ'ié/{X :, €fifikc ; é‘fim? ”j/C (b) /tan 31: d2: "" girl“: 3,34 a 4 W“ 5:? x ii“ @693 ix {553 3 xi Present your solutions clearly. 3 3. (15 points) Let ($2 + Deg”+2 y: x/cc~1 Find gfi using logarithmic differentiation. Express your answer in terms of only the variable :6. ‘fifinfi {37 fl Ewe :“iéiés’ $8,653 Jag/j; Qm(x2«éi>%/gm{€x+g)wfiwé><”j ‘3 £1(X2*137L 55’3“}; wfiéfi(xxi) g}, ,1- X9 2% j 37 2:: "" ”Xe-x, +/ W m sag .412” L ; )(W a?” G” ”H ”H ”376) W/ 4. (10 points) Find the area of the region enclosed by the curves y = cossc, y z %, and the y—axis. L9§f}: ,, w? in «i :fl Present your solutions clearly. 4 5. (10 points) Let A be the region in the first quadrant enclosed by the graphs of y = :02 + 1, :c = 1, and the coordinate axes. In the figure above, draw a picture representing the solid generated by rotating the region A about the x-axis. Set up but DO NOT EVALUATE all definite integrals needed to find the volume of this solid. it (Size {>1 64225 6. (10 points) Let A be the region enclosed by the graphs of a: = 1/2 + 1 and :c = 2. In the figure above, draw a picture representing the solid generated by rotating the region A about the y-axis. Set up but DO NOT EVALUATE all definite integrals needed to find the volume of this solid. Present your solutions clearly. 5 7. (10 points) Set up but DO NOT EVALUATE all definite integrals needed to find the length of that part of the graph of y z 2:2 - 2 below the line y = as. in am seem : ,3 i {322%} ”war*?:[email protected] . {"$'»;'li%+i>?é%t y’:2{«~l 133252; if: f, ) ~ M \l" {Arélflmfigflfl’ J :3 94(3}?1 gly «J 8. (15 points) A 20—foot metal chain weighing 10 pounds per foot is being lifted in a fashion illustrated below. begin during end I I 0 i i i i i i i i i i i i 5 Ci] I i T i y '3 l Find the work needed to lift the chain from the beginning position to the end. Do this by dividing the Chain into into slices of width Ay, letting y be the distance from a particular slice to the ground, and setting up a definite integral with respect to y. mew/Li“ at $215 1") l9 . 339 {£13} <9 «Hag (3me WM {7; iféufr {3% Egg 5y? W??? fixiwéeir} 35 i8~§§ 1{;§’l{)> W . (z 2.5:; f( ,l .l ‘t w [(3 \ [2653/1- l :: §§~fage~~noalagwufigl ...
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