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Section Solutions

Vector Fields, Curl, and Divergence

  1. no sketch

  2. no sketch

  3. no sketch

  4. no solution

  5. g(x,y)=exy+x2βˆ’y2

  6. g(x,y)=exsin(y)

  7. yes, g(x,y)=x2y

  8. yes, g(x,y)=ysin(x)

  9. yes, g(x,y,z)=exsin(z)+xyz+12y2+13z3

  10. no solution

  11. no solution

Line Integrals over Scalar Fields

  1. 0

  2. 8/3

  3. βˆ’βˆš2

Line Integrals over Vector Fields

  1. 69/2

  2. βˆ’69/2

  3. 3Ο€/4

Divergence Theorem and Green's Theorem

  1. If both sides are equal, you probably have the right answer!

  2. 81Ο€/2

  3. βˆ’256/15

  4. no solution

Divergence Theorem in Three Dimensions

  1. Hopefully you got the same answer both ways!

  2. Hopefully you got the same answer both ways!