practice3b

practice3b - 18.02 PRACTICE MIDTERM#3B BJORN POONEN Please...

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Unformatted text preview: 18.02 PRACTICE MIDTERM #3B BJORN POONEN 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 instructor’s last name: Recitation time (e.g., 10am): (Do not write below this line.) 1 out of 21 2 out of 15 3 out of 15 4 out of 15 5 out of 20 6 out of 14 Total out of 100 1) For each of (a)-(c) 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) Let F be a continuously differentiable vector field on R 2 , and let C be a simple closed oriented curve. If div F = 0 at every point inside C , then H C F · d r = 0. (b) Any region obtained by removing a ray (half-line) from R 2 is simply connected. (c) Let C r be the circle of radius r centered at (0 , 0), oriented counterclockwise. If F is a continuously differentiable vector field defined everywhere except (0...
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practice3b - 18.02 PRACTICE MIDTERM#3B BJORN POONEN Please...

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