Math 1920, Prelim 1October 2, 2008, 7:30 PM to 9:00 PMYou 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 whenyou 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 equationx+ 2y+ 3z= 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 functionr(t) = (cost)i+ 2tj+ (sint)k,wheret≥0.For eachtcalculate the angle between the velocity vector and acceleration vector.3) (14 points) The equation3x2y+yz+zln(2x-1) = 0definesxas a function of the two independent variablesyandz. Find the partial derivative∂x/∂zat the point (1,-1,-3).4) Letf(x, y) =1x2+y2-1.a) (5 points) Determine the domain off(x, y).b) (6 points) Determine and graph level curves in thex-yplane forf(x, y) =-2,1, and 2.
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