a). We can use the equation of a curve in polar coordinates to compute some areas...
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a). We can use the equation of a curve in polar coordinates to compute some areas bounded by such curves. The basic approach is the same as with any application of integration: find an approximation that approaches the true value. While doing some experiment, a class of mathematicians came up with a figure with a polar region R, as shown in the figure below. Find the area A of the polar region R. R Ae b). Prove that lim ffx'y'dxdy = 0. 00 c). Sketch (Using Mathematica) and find the volume of the curve formed by the cylinder x=-cos y, sys, on the top of the plane z=-2x, and below by the xy- plane. d). Use spherical coordinates to find the volume of the solid bounded below by the hemisphere p=1, z20, and above by the cardioid of revolution p=1+cosø. Sketch the region using Mathematica. a). We can use the equation of a curve in polar coordinates to compute some areas bounded by such curves. The basic approach is the same as with any application of integration: find an approximation that approaches the true value. While doing some experiment, a class of mathematicians came up with a figure with a polar region R, as shown in the figure below. Find the area A of the polar region R. R Ae b). Prove that lim ffx'y'dxdy = 0. 00 c). Sketch (Using Mathematica) and find the volume of the curve formed by the cylinder x=-cos y, sys, on the top of the plane z=-2x, and below by the xy- plane. d). Use spherical coordinates to find the volume of the solid bounded below by the hemisphere p=1, z20, and above by the cardioid of revolution p=1+cosø. Sketch the region using Mathematica.
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Related Book For
Introduction to Chemical Engineering Thermodynamics
ISBN: 978-0071247085
7th edition
Authors: J. M. Smith, H. C. Van Ness, M. M. Abbott
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