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Surface and Partial Derivatives

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Consider the function f (x, y) given by f (x, y) = ( 1 - x^2 - y^2)^2.

a) Sketch the graph of the curve f (x, 0) for x e [-2,2].
b) Sketch the level curves for f (x, y) = c for c = 0, c = 1/4, c = 3/4 and c = 2. Also plot the level set for f (x,y) = 1.

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