math142 s06 exam1 - 1M wVVEQM5 Math 142 Examl I Name Auk U...

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Unformatted text preview: 1M —; wVVEQflM5 Math 142 Examl I' Name Auk”; U V I 1. 13 pts Find the volume of the solid generated by revolving the region between the graphs of the functions 3; = 2:1: and 1; =32 about the line 3/ = -2. z u_ _ fix " 1'“ _. ,3___[t_u t, i ' “x”, 2. 12 pts Determine the surface area of the solid generated by revolving about the z—axis, e region I bounded the lines. :1: = — E = g, y = 0 and the graph of the function f = — ‘7’? v " 6 ' S s [W “W Mt“®:J_(€1-VT’)&M , ~11, 2 4. 18 pts 5. 10 pts Suppose f (z) z 3.11:2 + 1. Find all points c e [—5,—2] which are guaranteed by the Mean Value Theorem for Integrals for this function and interval. b m Ax (are an (‘ 2) ' ‘2' 1 W5 “WW , \ J (’x I?) V_ D \ \ / j x": ,. (I , r I t W I IE I. I _ 23x, - J \ r , ~ U My )_, -, {.30 x r J 77 x pLo)"/m 0’ [3 Va Cjéj—ngp- m Lox 4o “it-mm (ex :40, at <0 3 6. 17 pts The r ctangular plate with v t1ces at (3,2), (5,2), (3,7) and (5,7) has density at each / point equal to the distance from the y—axis to the point. Determine (a) the centroid of the 1 . plat and (b) the center of mass of the plate. a A ‘i / _ ‘ 1 . —-9L«m OJ my, C“ gmme 7. 18 pts A tank has the shape of the surface generated by revolving the parabolic segment 3; = 332, 0 g z 5 1 about the y—axis. If the tank is full of water, find the work required to pump the contents of the tank to a, level 7 feet above the top of the tank. Assume the dimensions of z and y are given in feet. ...
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