Math213H-F11-midterm2-v2

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Unformatted text preview: function at point (1,1), and use it to estimate f(1.2, 0.9) d. Use the quadratic approximation to find a better estimate for f(1.2, 0.9) 3. (18 pts) Consider the surface F ( x, y , z ) 5 x 3 y 2 3 xye z z 1 a. Find the plane tangent to this surface at point (1, 1, 0) b. Use implicit differentiation to find z z 2 z (1,1) , (1,1), and (1,1) x y y 2 4. (16 pts) Find the local maxima, minima and saddle points of f ( x, y ) 2 x 3 2 y 3 9 x 2 3 y 2 12 y . 5. (16 pts) Find the extreme values of the function f ( x, y, z ) xy z 2 on the curve of intersection of the plane z x y and the sphere x 2 y 2 z 2 4 6. (16 pts) Sketch the region of integration, reverse the order of integration, and evaluate the integral: 3 1 0 x /3 3 e y dy dx...
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## This document was uploaded on 02/27/2014 for the course MATH 213 at NJIT.

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