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math142 s06 mock exam

math142 s06 mock exam - < CLW Math 142 I David Mintz Mock...

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Unformatted text preview: < CLW Math 142 I: David Mintz Mock Exam 1. Finfithe area ot‘the region bounded by the given curves. 10 pts yzlsinx, yz—cosx, x20, x=zr gfl 2. Find the volume of the solid obtained ’ v rotating the region bounded by the given curves about the specified axis. 16 pts about the x-axis a g WWW“) " 5 ' . ' Lj . {it I}! It ' —-— \ 373 2, 3 - Tip X't cwgdrxfl x! L l J 'I ' - E i ‘1 ,7 TV 3.. .1. l— , '2 I" J: 2. 2 3 3. A force of30 N is required to maintain a spring stretched from its natural length of 12 cm to a length of 15 cm. How much work is done in stretching the spring from 12 an to 20cm? 20pts. EON—$105k \b: \000 8 2. .08 ID —--—- \N: momsz [FCC L D O onto 3. Find the average value ofthe function f(x) = xzw/l + x3 on the interval [0, 2]. 10 pts \ ME I 4. 3. Find the length ofthe curve y 2 %~ + T 4.x a K Rd V. ‘ 3 / \E e; rd! ‘ i- " E: t w \ '2 1" 2 4 if} n I 7x 3 w ,L . {‘1' ‘I h‘ i J... HI‘ \\ KJfl ,L 2. r - x .v, ‘"’ 2 ( 1.9—) ms \. L z '- ,v it?" \ \_ (f L€+ u: | +ij annlbd:vgmeax' Z [(0)2‘ \L(Z):G\ Imffii—a MC“ gig» I 20pts 1 ‘ X \ 'fOG': fif“£;i ‘ 1 _ 21 xi 1" 2% L ?Qw:wh -Mggaw w- (I. 11 .e_._.._ @x" ' x. 3 Ar “'2 I 4' fiF * \ a 5751 ' E? 713/ l . ~L+Q§ \ 4?: 4?? J f D I Plot? is bounuea DV 5 lines: x = 0.)» = 0. and 4 —y : . The densitv ofthe material of which the plate is constructed has a value of 3y at the point (x, y). What IS the centroid ot'the plate? What is the center of mass of the plate? 24 pts ...
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