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Section Solutions

Vector Fields, Curl, and Divergence

  1. no sketch

  2. no sketch

  3. no sketch

  4. no solution

  5. \(g(x,y) = e^{xy}+x^2-y^2\)

  6. \(g(x,y) = e^{x}\sin(y)\)

  7. yes, \(g(x,y) = x^2y\)

  8. yes, \(g(x,y) = y\sin(x)\)

  9. yes, \(g(x,y,z) = e^x\sin(z) + xyz + \frac{1}{2}y^2 + \frac{1}{3} z^3\)

  10. no solution

  11. no solution

Line Integrals over Scalar Fields

  1. \(0\)

  2. \(8/3\)

  3. \(-\sqrt{2}\)

Line Integrals over Vector Fields

  1. \(69/2\)

  2. \(-69/2\)

  3. \(3\pi/4\)

Divergence Theorem and Green's Theorem

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

  2. \(81\pi/2\)

  3. \(-256/15\)

  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!

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