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Unformatted text preview: 1. (20) True/False. No reasons need to be given. t For any nonzero real a and b , the vectors a i + b j and b i a j are orthogonal. f Proj ¯ w ¯ v always has the same direction as ¯ w . (It could be pointing in the opposite direction.) f The gradient ∇ f is normal to the surface z = f ( x, y ) at every point on the surface. (The surface in question is the level surface of the function z f ( x, y ) so its normal vector is h f x , f y , 1 i f The domain D of the function f ( x, y ) = 1 / ( x 2 y ) is a closed region. t The function f ( x, y ) = sin y + xe y has no local or absolute extrema. t The punctured plane { ( x, y )  ( x, y ) 6 = (0 , 0) } is a connected region but not simply connected. f H y d x + x d y x 2 + y 2 = 0 around every closed curve C containing the origin. (Green’s theorem doesn’t apply because the domain isn’t simply con nected, can do work integral around a circle centered at origin and get 2 π .) t H y d x + x d y x 2 + y 2 = 0 around every closed curve C not containing the origin....
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This note was uploaded on 09/23/2007 for the course MATH 1920 taught by Professor Pantano during the Fall '06 term at Cornell.
 Fall '06
 PANTANO
 Math, Multivariable Calculus, Vector Calculus, Vectors, y dx+x dy, 2yz cos yz

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