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Unformatted text preview: f at the point P (1 , 3 , 2) in the direction of the vector 2 , 1 , 1 ; (iii) the equation of the tangent plane at P to the level surface of f through P . 5. Use the method of Lagrange multipliers to Fnd the maximum and minimum values of f ( x, y, z ) = 2 x + 3 y z on the ellipsoid 4 x 2 + y 2 + 2 z 2 = 42. ind also the points where the maximum and minimum values are obtained. 6. ind the volume of the solid under the surface z = 6 + x + y 2 and above the region bounded by y = x and x = 2 y 2 . 7. Use polar coordinates to evaluate D y dA where D is the region in the Frst quadrant inside the circle x 2 + y 2 = 4 and outside the circle x 2 + y 2 = 2 x ....
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- Spring '09