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MAT397-2008Fall - MAT 397 FINAL EXAM Student ID NAME Circle...

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MAT 397 FINAL EXAM, Decembcr 10, 2008 Student ID: NAME: Circle your instructor's name: Bleier Coman CraÌ-¡bc Kovalev Lu Verchota Write your answers and sìrow all youl wolk on this tcst. Thele are 9 problerns on 9 pages (including this covel sheet), for a total of 100 points. To receive full or partial credit, the co¡¡ect rvorh leading to the coÌr'ect answel rnust be wlitten down. Ursu¡rpolted arrswers wiìl roceive little ol uo credit. Graphics calculatols may bc usccl. Symboìic calculators, such as TI-89 or TI-92, may not be used. .t,ro Iem Score 1 10 ,2 10 , t) 10 4 10 5 15 6 10 7 10 B 15 9 10 Total ( 100 )
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2 1.(10points) Fir:icl an equation for the plare cotrtairing the poiuts (1, -4, - 1), (2, 5, 4) and (-1,-7,-2) 2.(10 points) Com¡ntc the angle between the vectors a: (-3, a) and b - (f ,2)
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3,(10 points) Given lhe culve with vectoÌ equation r(¿) :3sin¿i + 3cos¿j -l- 41.k, fild tho following: (a) The unit tatrgerìt vectoÌ lo tìle curve at thc point where /: n. (b) Thc length of the arc oI the curve where 0 ( ú ( 1
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4 4.(10 points)
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