midterm4

# midterm4 - 18.02 MIDTERM#4 BJORN POONEN December 3 2010...

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18.02 MIDTERM #4 BJORN POONEN December 3, 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 10 3 out of 20 4 out of 35 5 out of 25 Total out of 100

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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.) If you are looking at a ﬂat disk S in R 3 , and its chosen unit normal vector is pointing straight at you, then the compatible orientation of its boundary curve would appear from your vantage point to be counterclockwise. (b) (5 pts.) If F = h P,Q,R i is a continuously diﬀerentiable 3D vector ﬁeld on R 3 such that Q x = P y , then F = f for some function f ( x,y,z ) deﬁned on R 3 .
2) Let C be the straight line path from (0 , 0 , 0) to (2 , 3 , 5). Evaluate Z C x 2 y dz .

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midterm4 - 18.02 MIDTERM#4 BJORN POONEN December 3 2010...

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