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Final_mock

# Final_mock - Mock Final Exam Multivariable Calculus Math...

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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 non-zero vectors in R 3 and a · b = 0, then a × b = 0 . (2) Let f be a function in two variables. If f x ( x 0 , y 0 ) = f y ( x 0 , y 0 ) = 0, then f has a local maximum or a local minimum at the point ( x 0 , y 0 ). (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 0 , y 0 ) is 0 if u is perpendicular to f ( x 0 , y 0 ). (9) lim ( x,y ) (0 , 0) x 2 - y 2 x 2 + y 2 exists. (10) If F is a vector field in R 3 , such that div F = 0, then the flux of F across any surface in R 3 equals 0.

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Final_mock - Mock Final Exam Multivariable Calculus Math...

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