Final_Fall_2008-2009 - Fall 2008-2009 Final Exam Date...

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Unformatted text preview: Fall 2008-2009 Final Exam Date: January 30 Prof: M. Egeileh Math 201 - Sections 17 to 20 Duration: 2 hours Exercise 1 (5 pts) Is the series X n > (- 1) n n ! convergent ? absolutely convergent ? Justify your answers. Exercise 2 (5 pts) Does lim ( x,y ) → (0 , 0) x 2 x 2- y 2 exist ? Justify your answer. Exercise 3 (17 pts) We consider the function defined on R 2 by : f ( x, y ) = x 2 + 2 y 2- y 3 3 . 1. Find all the critical points of f . (4 pts) 2. Give the nature (local minimum, local maximum or saddle point) of each of the critical points you found in question 1. (8 pts) 3. Give an equation for the tangent plane to the graph of f at the point (0 , 4 , f (0 , 4)). (5 pts) Exercise 4 (35 pts) Let R be the region in the plane bounded by the triangle of vertices O (0 , 0), A (2 , 0) and B (1 , 1). We denote by C 1 the line segment joining O to A , C 2 the line segment joining A to B , and C 3 the line segment joining B to O ....
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Final_Fall_2008-2009 - Fall 2008-2009 Final Exam Date...

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