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Unformatted text preview: , 1 , 1) , (1 ,1 , 1) , and (2 , 3 , 0). (b) (5 points) Find the area of the triangle with vertices (1 , 1 , 1) , (1 ,1 , 1) , and (2 , 3 , 0). 4. (a) (6 points) Draw (and clearly label) four traces of the function f ( x, y ) = x sin( y ) (b) (2 points) Which of the following is the graph of f ( x, y ) = x sin( y )? (a) (b) (c) (d) 5. (5 points) Set up, but do not evaluate the integral which gives the arclength of the space curve r ( t ) = < t 3 , e 4 t , 2 cos( πt ) > between the points (0 , 1 , 2) and (8 , e 8 , 2). Bonus: (5 points) What is the curvature of the space curve r ( t ) = < (sin √ 3 t 13 ) t , 4(sin √ 3 t 13 ) t , (sin √ 3 t 13 ) t > at t = 1?...
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 Fall '07
 Crow
 Math, #, Parametric equation

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