FinalExam-sample - FINAL EXAM Math 251 Name: PROBLEM 1 (5...

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Unformatted text preview: FINAL EXAM Math 251 Name: PROBLEM 1 (5 pts): Find the equation of the plane containing the points (1 , , − 1) , (1 , 1 , 2) and ( − 1 , 2 , 9). PROBLEM 2: The two space curves vector r 1 ( t ) = ( t + 1 , t 2 − 2 t + 2 , 2 t ) and vector r 2 ( s ) = ( 2 s, s 3 − 2 s + 1 , 5 s − 4 ) intersect in exactly one point. a (3 pts): Find the point of intersection and the values t and s that give this point for vector r 1 and vector r 2 respectively. b (3 pts): Find the angle between the vectors vector r 1 ′ ( t ) and vector r 2 ′ ( s ). PROBLEM 3 (12 pts): Find the points of maximum and minimum cur- vature for the curve vector r ( t ) = ( e t )ˆ ı + ( t )ˆ on the range − 2 ≤ t ≤ 2. PROBLEM 4 (12 pts): At the point ( − 2 , 7) a certain function f ( x, y ) has gradient ∇ f ( − 2 , 7) = (− 4 , 12 ) . Find two unit vectors (directions) for which the directional derivative of f at P = ( − 2 , 7) is equal to 4....
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This note was uploaded on 11/16/2011 for the course MULTIVARIA 251 taught by Professor Staff during the Fall '11 term at Rutgers.

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FinalExam-sample - FINAL EXAM Math 251 Name: PROBLEM 1 (5...

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