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Unformatted text preview: , 1), (6 , 1), and (4 , 3) in the xyplane. The density of the plate at each point is given by δ ( x,y ) = x + y . Write down an iterated integral whose value is the moment of inertia of the plate when it is rotated around the yaxis. Do not evaluate the integral! 4) Given that variables w,x,y,z satisfy the constraints w = xyz and w 2 + z 2 = 13, ﬁnd the value of ± ∂w ∂x ² y when w = 3, x = 3, y = 1 / 2, and z = 2. 5) Use Lagrange multipliers to ﬁnd the point(s) on the curve x 4 + y 4 = 32 closest to the origin. (Make sure to show that you have checked everything that you need to check.) This is the end! Scratch work, or continuation of work on problem number (Detach and recycle this page if it is not part of your solutions.) Scratch work, or continuation of work on problem number (Detach and recycle this page if it is not part of your solutions.)...
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 Fall '08
 Auroux
 Multivariable Calculus, Force, Moment Of Inertia, Rotation, student ID number, BJORN POONEN

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