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Unformatted text preview: 1. (20) True/False. No reasons need to be given. – For any nonzero real a and b , the vectors a i + b j and b i a j are orthogonal. – Proj ¯ w ¯ v always has the same direction as ¯ w . – The gradient ∇ f is normal to the surface z = f ( x, y ) at every point on the surface. – The domain D of the function f ( x, y ) = 1 / ( x 2 y ) is a closed region. – The function f ( x, y ) = sin y + xe y has no local or absolute extrema. – The punctured plane { ( x, y )  ( x, y ) 6 = (0 , 0) } is a connected region but not simply connected. – H y d x + x d y x 2 + y 2 = 0 around every closed curve C containing the origin. – H y d x + x d y x 2 + y 2 = 0 around every closed curve C not containing the origin. – If f ( x, y, z ) is harmonic everywhere (i.e. f xx + f yy + f zz = 0), then the outward flux of ∇ f across a smooth, closed, oriented surface S is always 0. – Let ¯ F be a vector field with continuous first partials everywhere....
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 Fall '06
 PANTANO
 Derivative, Multivariable Calculus, Vector Calculus, Vectors, Manifold, Orientability, y dx+x dy

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