extra - Math 1920 Challenge problems 1 Given the line plane...

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Unformatted text preview: Math 1920 - Challenge problems 1. Given the line, plane, and paraboloid, . line : x- 2 = y- 4 = 8- z 2 . plane : ( x + 2) + 2( y- 2) + ( z- 4) = 0 . paraboloid : z = 1- x 2- y 2 set up a systems of equations that will give you the answer, but do not solve! (a). Find the shortest distance between the paraboloid and the plane. Use vectors and a geometric argument. (b). Find the shortest distance between the paraboloid and the plane. Use a minimization argument. (c). Find the shortest distance between the paraboloid and the line. Use vectors and a geometric argument. (d). Find the shortest distance between the paraboloid and the plane. Use a minimization argument. 2. (a) Solve the integral Z 1- 1 Z 1- 1 | y | x 2 + y 2 dy dx (b) Does the integral converge? If so, to what value? 3. (a) Solve the integral Z ∞-∞ Z 1- 1 | y | x 2 + y 2 dy dx (b) Does the integral converge? If so, to what value? (c) Convert the integral to polar coordinates. 4. A flat plate is defined by the area between the curves y = x 2 and y = x . The density of the plate is f ( x,y ) = 1. (a) Draw the plate (be sure to label everything properly). (b) Find the mass of the plate. (c) Find the center of mass for the plate....
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extra - Math 1920 Challenge problems 1 Given the line plane...

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