Practice Final Exam Solutions - Accelerated Multivariable Calculus Harvard University - MATH 2413Practice_final_exam_solution. ALL ANSWERS CORRECT

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Practice Final Exam Solutions - Accelerated Multivariable Calculus 1. Determine whether the following are TRUE or FALSE, and write your answer into the box. a) If ~a ×~b = ~0, then either one (or b... oth) of the vectors is zero, or ~a and ~b are parallel. TRUE b) Let the components of the vector field F~ = hP; Q; Ri have continuous second order partial derivatives. Then div curl(F~ ) = 0. TRUE c) If a function f(x; y) is differentiable at (a; b) and rf(a; b) = ~0, then f has either a local maximum or a local minimum at (a; b). FALSE d) The line integral RC f(x; y)ds depends on the orientation of the curve C. FALSE e) If a function f(x; y) has continuous first order partial derivatives, then the surface, given by the equation z = f(x; y), has a unique tangent plane at each point. TRU [Show More]

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