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Unformatted text preview: MAC 2313 Nov 16, 2010 Exam III Prof. S. Hudson Show all your work and reasoning for maximum credit. Do not use a calculator, book, or any personal paper. You may ask about any ambiguous questions or for extra paper. Hand in any extra paper you use along with your exam. These are 10 points each, except the TF is 20pts, total. 1) Find a unit vector in the direction in which f decreases most rapidly at P , and find the rate of change of f at P in that direction; f ( x,y ) = cos(3 x y ); P ( π/ 6 ,π/ 4). 2) Express the integral as an equivalent integral with the order of integration reversed; R 2 R √ x f ( x,y ) dy dx . 3) Evaluate the iterated integral by converting to polar coordinates; R 1 R √ 1 x 2 ( x 2 + y 2 ) dy dx . 4) Find an equation for the tangent plane and parametric equations for the normal line to the surface z = 4 x 3 y 2 + 2 y at the point P (1 , 2 , 12). 5) True  False: Let T be the triangle with vertices at (0 , , ) (1 , 1) and (2 , 0). Which of the following are equivalent to...
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 Fall '06
 GRANTCHAROV
 Derivative, dy dx, Spherical coordinate system, Multiple integral

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