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# fin_2007F - Math 210 Calculus III Final Exam Thursday YOU...

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Math 210, Calculus III Final Exam, Thursday December 13, 2007 YOU MUST SHOW ALL OF YOUR COMPUTATIONS IN THE EXAM BOOKLET TO RECEIVE FULL CREDIT. Make clear what your answer to each question is. You may find the fact that integraldisplay 2 π 0 cos 2 ( t ) dt = π useful. 1. (a) Compute the integral contintegraldisplay C −→ F · d −→ s where C is the circle x 2 + y 2 = 1 of radius 1 centered at the origin, traversed counterclockwise, starting and ending at the point (1 , 0) for −→ F = ( P, Q ) = (bigg y x 2 + y 2 , x x 2 + y 2 )bigg (b) For the vector field in part (a), we know that ∂P ∂y = ∂Q ∂x ( you are not to check this! ). Is −→ F conservative? Explain your answer. 2. A particle is traveling in R 3 , with position given at time t , for 0 t 3 by −→ r ( t ) = (big 1 + t, e t , t 2 )big (a) find the velocity of the particle at time t (b) find the speed of the particle at time t (c) find the acceleration of the particle at time t (d) Write down an integral, but do NOT attempt to compute it , for the distance traveled by the

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fin_2007F - Math 210 Calculus III Final Exam Thursday YOU...

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