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Unformatted text preview: g ( x, y, z ) = x 4 + y 4 + z 4 = 1. 6 6. Let z = x 2 + xy 3 , x = uv 2 + w 3 , and y = u + ve w . Use the Chain Rule to ﬁnd ∂z ∂v , when u = 2 , v = 1 , w = 0. 7 7. Find all the points at which the direction of the fastest change of the function f ( x, y ) = x 2 + y 22 x4 y is i + j . 8 8. Find the absolute maximum and minimum values of f ( x, y ) = x 2 + y 2 + x 2 y +4 on the region D = { ( x, y )   x  ≤ 1 ,  y  ≤ 1 } . 9 9. Evaluate the triple integral R R R E z dV , where E is bounded by the cylinder y 2 + z 2 = 9 and the planes x = 0 , y = 3 x, and z = 0 in the ﬁrst octant. 10 10. Evaluate the triple integral R R R E x 2 dV , where E is the solid that lies within the cylinder x 2 + y 2 = 1, above the plane z = 0, and below the cone z 2 = 4 x 2 + 4 y 2 . 11...
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This note was uploaded on 10/26/2010 for the course MATH 20D 0382332 taught by Professor Edgars during the Spring '10 term at UCSD.
 Spring '10
 Edgars

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