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Unformatted text preview: Math 241 Exam 3 Version 1 1. (5pts) Determine if the following statement is true or false. You do not need to justify your answer. For each part, you will receive 1 point for a correct answer,- 1 point for an incorrect answer, and 0 points for no answer. Everyone starts with 1 total point and the lowest possible total score on this problem is zero. (a) Z 2 Z x 3 dydx = Z 2 Z y 3 dxdy . (b) Z 1- 1 Z 3 x 2 e x + y dydx = Z 1- 1 x 2 e x dx Z 3 e y dy (c) If F is a vector field, then curl F is a vector field. (d) When transforming a double integral in xy-coordinates to one in uv-coordinates, you need formulas for u and v in terms of x and y . 2. Let F ( x,y ) = (3 x 2 y 3 + 6 x, 3 x 3 y 2- 6 y 2 ). (a) (2pts) Explain why the vector valued function F is called a vector field. (b) (3pts) Find the divergence of F . (c) (2pts) Is the vector field F incompressible? Briefly justify your answer....
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This note was uploaded on 02/15/2011 for the course MATH 241 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.
- Spring '08