prelim1Sping2005 - ATTENTION, Fall 2005 students: Ignore...

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ATTENTION, Fall 2005 students: Ignore problems 4,5 and 8 which refer to material not covered in your first prelim Math 192, Prelim 1 February 22, 2005 You are allowed one 8 . 5 × 11 sheet of paper. You are NOT allowed calculators or the text. SHOW ALL WORK! 1) a) (5 points) Find two vectors ~ A and ~ B such that ~ A × ~ B = ~ i + ~ j . b) (5 points) Find a unit vector ~ A such that ~ A · ( ~ i + 2 ~ j - 3 ~ k ) = 0. c) (5 points) Find the area of the triangle with vertices (1 , 0 , 0), (0 , 2 , 0), and (0 , 0 , - 3). 2) (12 points) Let ~ r ( t ) = 3 t 2 ~ i + sin( πt/ 2) ~ j + ln ( t ) ~ k . Find the equation of the tangent line to the curve at the point (3 , 1 , 0). 3) Let f ( x, y ) = sin x y . a) (5 points) Plot the level curves c = f ( x, y ) for c = 1 , - 2. b) (5 points) Find lim ( x,y ) ( π, 1) f ( x, y ) or show it does not exist. c) (5 points) Find lim ( x,y ) ( π, 0) ,y 6 =0 f ( x, y ) or show it does not exist. 4) A function
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