Practice Final - proportional to the distance from that point to the center of the base a Calculate the mass of the solid b Calculate the center of

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2401 Practice Final: Fall 2005 Written by Adam Tart 1) Given an ellipse in the form: x 2 + 25 y 2 = 25 a) Parameterize the ellipse b) Find the unit tangent and principal normal vectors at the point (3, 4/5) c) Find the curvature at the point (3, 4/5) d) Find the tangential and normal components of acceleration at the point (3, 4/5) 2) Give the surface z = x 2 + y 2 – 6 x – 4 y + 14 a) Find the local min b) Find the equation of the tangent plane at the local min 3) Given a hemisphere of radius 2, with the center of its base at the origin, and no points below the xy -plane. The mass density at any point in or on the hemisphere is directly
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Unformatted text preview: proportional to the distance from that point to the center of the base. a) Calculate the mass of the solid. b) Calculate the center of mass of the solid. 4) Calculate the following line integral over the curve C that is the boundary of the region between the curves y = x and y = x 2 a) Directly b) Using Green’s theorem 5) Find the surface area of the cone z 2 = x 2 + y 2 from z = 3 to 4. 6) Find the flux of the vector field v = i + 2 j + k out of the sphere x 2 + y 2 + z 2 = 4...
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This homework help was uploaded on 04/09/2008 for the course MATH 2401 taught by Professor Morley during the Spring '08 term at Georgia Institute of Technology.

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