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Unformatted text preview: Mock Final Exam Multivariable Calculus Math 53M, 2001. Instructor: E. Frenkel 1. For each statement below, determine whether it is true or not. Circle T if it is true, or F if it is false. (1) If a and b are two nonzero vectors in R 3 and a b = 0, then a b 6 = . (2) Let f be a function in two variables. If f x ( x , y ) = f y ( x , y ) = 0, then f has a local maximum or a local minimum at the point ( x , y ). (3) There exists a vector field F , such that curl F = x 3 i + y 3 j + z 3 k . (4) There exists a vector field F , such that div F = x 3 + y 3 + z 3 . (5) The line integral of the vector field x i over any closed curve in R 3 equals 0. (6) Any surface in R 3 , which belongs entirely to the yz plane is orientable. (7) The flux of any vector field across any closed surface in R 3 without boundary equals 0. (8) The directional derivative D u f ( x , y ) is 0 if u is perpendicular to f ( x , y )....
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This note was uploaded on 03/09/2010 for the course PHYSICS 7A taught by Professor Lanzara during the Fall '08 term at University of California, Berkeley.
 Fall '08
 Lanzara
 Physics

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