MAT397-2006Fall - M ath 397 F all 2006 Final Exam P roblem...

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Math 397 Fall 2006 Final Exam Name: _ (Please Print.) Do all your work on this exam. Correct answers should be supported by your calculations and reasoning where appropriate. McCaffrey Pelley Quinn !Circle the Name of your Instructor:1 Shen Zhang x = 3+ t 1. (a) Find the point where the line y =2 - 3t - 00 < t < 00 meets the z = 1+ 2t plane 2x + y + z = 4. Problem Points Score 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 8 9 8 10 10 11 8 12 10 Total 100 (b) Find equation of the plane containing the intersecting lines x =2 + t x + 2s y = 4- 3t and y=4+s -oo<s<oo. z = 1 + 2t Z = 1- 2s
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r(t)=e ti--J2tj+e- tk, 2.< Find the length of the curve given by the vector valued function Os t s In 3. 3. A particle moves with velocity vector vet) = e' i + sint j + 2t k at time t. At time t =0 its position vector is reO) = 2 i + 3 j - k. Find its position vector ret) at time t.
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4., Compute the following limits: (a) Lim 3xy (x,y)~(O,O) x 2 + 2y2 xy-2y+ 3x-6 (b) Lim (x,y)--(2,3) xy-2y 3y x 5. (a) Find the linearization of the function !(x,y) = e - at the point P(3,1), (b) Find the direction in which the function !(x,y,z) = 2xy2 + xy2 increases most rapidly at the point Q(3,-1,l) and find that rate of increase.
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6." Find and
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MAT397-2006Fall - M ath 397 F all 2006 Final Exam P roblem...

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