Disc4 - Math 170 Kouba Discussion Sheet 4 1.) Let R be the...

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Unformatted text preview: Math 170 Kouba Discussion Sheet 4 1.) Let R be the region bounded by the graphs of y = 3:2 and y = 3x . a.) Describe R using vertical cross-sections. b.) Describe R using horizontal cross—sections. 2.) Let R be the region inside the circle of radius 5 centered at (3, 4) and to the right of the line a; = 3. a.) Describe R using vertical cross-sections. b.) Describe R using horizontal cross-sections. 3.) Let R be the triangular region with vertices (0,0), (2,0), and (3,2). a.) Describe R using vertical cross-sections. b.) Describe R using horizontal cross-sections. 4.) Let R be the region bounded by the graphs of :1: = y2 and .z = y + 2 . Describe R using vertical cross—sections. b.) Describe R using horizontal cross—sections. 5.) Sketch each of the following regions described in two—dimensional space. a.)0§m§3,2§y§4 b.)0§m£3,\/§Sy§w+1 c.)1§m£3,0§yglnm d.)0$y$ln3,eyga:§3 8-) 03y51,y23wS4-—y 6.) Evaluate the following double integrals. /01 173/2 dydzr b.) [:2 /Omz(1/:c)cos(y/m) dydm (Beware of the next two.) 1 4 2 I 2 1 c.)//e‘y dyda: cos(x2)dmdy 0 4x 0 y/2 7.) Consider the tetrahedron with vertices (0, 0, O), (4, 0, 0), (0,3,0), and (0,0,2). It’s top surface is a plane. Find an equation for this plane. b.) Set up but do not evaluate a double integral which represents the volume of the . tetrahedron. ' Consider a flat plate lying in region R bounded by the graphs of :r = y3, a: = 8, and y 2 0. Assume that density at pont (13y) is given by 6(36, y) = 1 + my grams per square 1 inch. F indthe a.) average height of region R. average width of region R. average square of the distance from points (:13, y) in R to the point (0,4). b.) M d.) total mass of the plate. e.) average density of the plate. 9.) Sketch the solid in 3D—Space whose volume is given by the following double integrals. 3 2 a.) / / 4dy d1: 0 0 b.) [02/044116 — 2m —— (3/2)y) dy drr 2 W c.) / / (7—:c2-y2) dydzz: —2 —\/?1‘~E7 +++++++++++++++++++++++++++++++++ ”I have always observed that to succeed in the world one should appear like a fool but be wise.” — Charles de Montesquieu ...
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Disc4 - Math 170 Kouba Discussion Sheet 4 1.) Let R be the...

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