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Unformatted text preview: The University of Sydney School of Mathematics and Statistics Summer School MATH2061: Vector Calculus 2012 Assignment This assignment consists of five questions. Full marks will only be awarded where working is shown. One question is due in each of your first five tutorials. Attach an assignment cover sheet to your solution and hand in during your tutorial on the dates stated at the end of each question. 1. Let C be the curve described by the parametric equations x = sin 10 t cos t, y = sin 10 t sin t, z = cos 10 t, t : 0 2 . (a) Show that the length of C is given by integraldisplay 2 radicalbig sin 2 10 t + 100 dt. (You do not have to evaluate the integral.) (b) Evaluate integraldisplay C ds radicalbig x 2 + y 2 + 100 . (Due in the tutorial Monday 30 January) 2. Calculate the work done by the force field F = 3 xy i + 5 y 2 j- 3 yz k (a) along the path from (1 , , 2) to (0 , 1 , 0); (b) counter-clockwise along the upper semicircle y = 1- x 2 in the xy-plane (so z =0)....
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