Mathematics 317 Midterm#3 _2009_1 - Mathematics 317 Midterm#3 Friday 1 Answer Question#1 Do only one of Questions#2 and#3 Each question is of equal

Mathematics 317 Midterm#3 _2009_1 - Mathematics 317...

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Mathematics 317 Midterm #3: Friday, November 20, 2009 1. Answer Question #1. Do only one of Questions #2 and #3. Each question is of equal value. No notes, books or calculators are permitted. 2. Time Limit: 50 minutes 1. Consider the vector field given by rF)(ρf=where ,,rkjir=++=ρzyx)(ρfis a continuous function of .0,ρρLet σbe the triangular surface with vertices (1,1,0), (1,0,1) and (1,1,1). (a) Set up a double integral (do not evaluate) to find the magnitudeof the flux of through the triangular surface σ(b) Evaluate the magnitude of the flux of Fthrough the triangular surface σin the case when .1)(=ρANSWER ONLY ONE OF THE NEXT TWO QUESTIONS. FOR EACH OF THESE QUESTIONS THE DIVERGENCE THEOREM MAY BE OF USE.2. Consider the vector field given by kjiF)1()()(232+++++-=zyzyxyzxβαwhere αand βare constants. Let C be the closed curve bounded by the straight line joining (-1,0,0) to (1,0,0) and the semi-circle .0,0,
and F . f
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