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Unformatted text preview: 18.02 MIDTERM #3 BJORN POONEN November 12, 2010, 2:05pm to 2:55pm (50 minutes). Please turn cell phones off completely and put them away. No books, notes, or electronic devices are permitted during this exam. Generally, you must show your work to receive credit. Name: Student ID number: Recitation leader’s last name: Recitation time (e.g., 10am): (Do not write below this line.) 1 out of 10 2 out of 20 3 out of 15 4 out of 35 5 out of 20 Total out of 100 1) For each of (a) and (b) below: If the statement is true, write TRUE. If the statement is false, write FALSE. (Please do not use the abbreviations T and F.) No explanations are required in this problem. (a) (5 pts.) Let R be the region obtained by removing the first quadrant from the plane, so R is the set ( x, y ) in R 2 such that x < 0 or y < 0 (or both); then R is simply connected. (b) (5 pts.) For every region R in R 2 and for every continuously differentiable vector field F defined on R , if F is the gradient of some differentiable function on R , then curl F = 0 at every point of R . 2) Find...
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This note was uploaded on 09/14/2011 for the course MATH 18.02 taught by Professor Auroux during the Fall '08 term at MIT.
- Fall '08
- Multivariable Calculus