Final_practice

# Final_practice - MATH53 with Prof. Frenkel Final Practice...

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MATH53 with Prof. Frenkel Final Practice GSI : Jae-young Park 108(MWF 1100-1200) 110(MWF 1200-0100) Name: Score: 1. (0 points) Final exam is on Dec 19 1230-0330 on Hearst gym (room 237 for section 108,110) Oﬃce hours(Evans 937): Dec 9 (W11-1) Dec 16(W 4-5)/ Dec 17(Th4-5) Dec 18(F3-6) You can ﬁnd the homeworks in front of my oﬃce. . I’ll send the answer key for this practice problem by email 2. (0 points) (conservative vector ﬁeld) Determine if -→ F = < 2 xz + y 2 , 2 xy,x 2 + 3 z 2 > is conservative or not. Also, compute R C -→ F · -→ dr where C is given by < cos t, sin t,t >, 0 t 2 π . 3. (0 points) (Green/line integral) For vector ﬁeld -→ F = 1 x 2 + y 2 < - y,x > , ﬁnd R C -→ F · -→ dr where C is an ellipse x 2 / 4+( y - 1) 2 / 9 = 1 with counter clockwise orientation. 4. (0 points) (Green) Let C denote the circle ( x - 2) 2 + ( y - 3) 2 = 4 in the xy -plane, oriented counterclockwise. Compute Z C (2 x + y 2 ) dx - (3 x - 2 xy ) dy 5. (0 points) (surface integral/center of mass) Let

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## Final_practice - MATH53 with Prof. Frenkel Final Practice...

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