Review Final

Review Final - MA 242 REVIEW I. Find the max-min-saddles...

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MA 242 REVIEW I. Find the max-min-saddles for a. f(x,y)= x 3 - 3 x 2 - 9 x + y 3 - 3 y. b. f(x,y)= x 3 - 6 xy + y 2 II. Find the flux through the closed surface bounded by y + z = 2 , y = x 2 and z=0 of a fluid with velocity F ( x, y, z ) = < z, z, z > The orientation is out. . III. Find the flux of the fluid with velocity F ( x, y, z ) = < z, z, z > through the part of surface y+z=2 that is inside x 2 + y 2 = 4. The orientation is up. IV. Find the work done by force F ( x, y, z ) = < z, y, x > along the path R ( t ) = < t 3 , t 2 , t > from (0,0,0) to (8,4,2) V. Let F(x,y,z)= x 2 - yz. P: (1,2,3) and v= < 2 , - 3 , 2 > Find a. The gradient to F at P. b. The rate of change in F in the v direction at P.
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