Math241PracticeTest1

Math241PracticeTest1 - f ( x, y ) = e x 2 + y 2 . Draw a...

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Math 241 Practice Test for Quiz 1, Linda Patton’s Course Covers Section 13.6, 13.7, 15.1, 15.2 Show all work! You may use a non-graphing calculator, but show all work beyond arithmetic by hand. Good luck. 1. (a) (5 points) Identify the traces and sketch the quadric surface given by y 2 = 4 x 2 + z 2 . (b) (5 points) Identify the traces and sketch the quadric surface given by x 2 + y 2 + 9 z 2 = 1 2. (a) (5 points) Convert the point (1 , - 3 , 2) from rectangular to spherical coordinates. (b) (5 points) Convert the point (5 , π 2 , π 3 ) from spherical to cylindrical coordinates. 3. (10 points) Find an equation in spherical coordinates for the sphere x 2 + y 2 + z 2 - 2 az = 0, where a > 0. 4. (10 points) Plot several level curves for the function
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Unformatted text preview: f ( x, y ) = e x 2 + y 2 . Draw a rough sketch of the graph of the function also. 5. (10 points) Let T ( x, y ) = 50 1+2 x 2 + y 2 describe the temperature of a point at ( x, y ) in the plane. (a) Sketch several level curves of the function. Describe in words what the level curve where k = 25 represents. (b) What is the range of this function? 6. (a) (5 points) Show that lim ( x,y ) → (0 , 0) x 3 y x 6 + y 2 does not exist. (b) (5 points) Does lim ( x,y ) → (1 ,-2) x 3 y x 6 + y 2 exist? Either explain why the limit does not exist or compute the limit....
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This note was uploaded on 05/19/2008 for the course MATH MATH 241 taught by Professor Patton,linda during the Spring '08 term at Cal Poly.

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