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Unformatted text preview: MTH 133 m Section 58 —— 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
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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
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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}:
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: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 xaxis. 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 yaxis. 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
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«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
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'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}
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 Fall '07
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