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practicefinalb

# practicefinalb - 18.02 PRACTICE FINAL EXAM B BJORN POONEN...

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18.02 PRACTICE FINAL EXAM B 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.)

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1 out of 20 2 out of 10 3 out of 10 4 out of 10 5 out of 10 6 out of 10 7 out of 15 8 out of 10 9 out of 10 10 out of 15 11 out of 15 12 out of 10 13 out of 20 14 out of 20 15 out of 10 16 out of 10 17 out of 10 18 out of 10 19 out of 25 Total out of 250 2
1) For each of (a)-(d) 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) The set of points ( x, y ) in R 2 satisfying x 2 + y 2 > 9 is simply connected. (b) If T is any region in R 2 , and F is a continuously differentiable 2 D vector field on T such that curl F = 0 at each point of T , then F is the gradient of some function on T . (c) If A is a 3 × 3 matrix such det A = 0, and b R 3 , then there is exactly one vector x such that A x = b . (d) If the position vectors a, b and c, d form two sides of a parallelogram, then the area of the parallelogram equals ad - bc .

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practicefinalb - 18.02 PRACTICE FINAL EXAM B BJORN POONEN...

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