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prelim1_fa08

prelim1_fa08 - Math 1920 Prelim 1 October 2 2008 7:30 PM to...

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Math 1920, Prelim 1 October 2, 2008, 7:30 PM to 9:00 PM You are NOT allowed calculators, the text or any other book or notes. SHOW ALL WORK! Write your name and Lecture/Section number on each booklet you use. You may leave when you have finished, but if you have not handed in your exam booklet and left the room by 8:45, please remain in your seat so as not to disturb others who are still working. 1) a) (7 points) Calculate the distance from (1 , 1 , 1) to the plane with the equation x + 2 y + 3 z = 0 . b) (7 points) Find the equation of the plane through (0 , 0 , 0) , (1 , 1 , 0), and (1 , 2 , 3). 2) (14 points) The position vector of a particle moving in space is given by the vector function r ( t ) = (cos t ) i + 2 t j + (sin t ) k , where t 0 . For each t calculate the angle between the velocity vector and acceleration vector. 3) (14 points) The equation 3 x 2 y + yz + z ln(2 x - 1) = 0 defines x as a function of the two independent variables y and z . Find the partial derivative ∂x/∂z at the point (1 , - 1 , - 3). 4) Let f ( x, y ) = 1 x 2 + y 2 - 1 . a) (5 points) Determine the domain of f ( x, y ). b) (6 points) Determine and graph level curves in the x - y plane for f ( x, y ) = - 2 , 1, and 2.
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