Math252FinalF08

Math252FinalF08 - Math 252 Name FINAL MATH 252 FALL 2008...

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Math 252 Name: ________________________ FINAL MATH 252 – FALL 2008 – KUNIYUKI 60 POINTS TOTAL (15 PROBLEMS; 4 POINTS EACH) No books allowed. An appropriate sheet of notes and a scientific calculator are allowed. 1) If a and b are vectors in V 2 such that a b < 0 , which of the following is true? Box in the best answer: a) The angle between a and b is in 0 ± ,90 ± ± ² ) . b) The angle between a and b is in 90 ± ,180 ± ( ± ² . c) a b tells us nothing about the angle between a and b . 2) Write an equation for the plane in xyz -space that is parallel to the plane with equation 3 x ± 2 y + 7 z = 10 and that contains the point 4, ± 1, 8 () . 3) Consider the graph of 4 x 2 ± 5 y 2 ± 6 z 2 = 3 in xyz -space. The trace of the graph in the plane x = 10 is … (Box in one): a) An Ellipse b) A Hyperbola c) A Parabola

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4) If r is a vector-valued position function of t that is smooth and twice differentiable for all real t , which one of the following will be true for all real t ?
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Math252FinalF08 - Math 252 Name FINAL MATH 252 FALL 2008...

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