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A7 - 2 0 to the cone deﬁned by z 2 = x 2 y 2 4 Find the...

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MATH 222, Calculus 3, Fall 2011 Assignment 7, due in class Monday, November 7, 2011 1. Your box has to be able to hold 40 m 3 of stuff. It does not need a top. Material for the sides is relatively cheap at \$1 per square meter; the bottom material is more expensive at \$10 per square meter. Being stingy, you want to make the box as cheaply as possible. What will be the dimensions of the box? 2. Find the maximum and minimum values of f ( x, y ) = x 5 y 3 on the circle defined by x 2 + y 2 = 10. Do the same for the disc x 2 + y 2 10. 3. Find the minimum distance from the point (1
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Unformatted text preview: , 2 , 0) to the cone deﬁned by z 2 = x 2 + y 2 . 4. Find the maximum and minimum values of f ( x,y,z ) = 3 x-y-3 z on the curve that is the intersection of the surfaces deﬁned by x + y-z = 0 and x 2 + 2 y 2 = 1. 5. Suppose that z = f ( x,y ), x = s + t and y = s-t . Show that z 2 x-z 2 y = z s · z t . 6. Suppose that z is deﬁned implicitly (as a function of x and y ) by z 3-3 xz + 3 xyz = 1. Find the partial derivatives ∂z ∂x and ∂z ∂y . When are they deﬁned? 1...
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