Test Postponed. The main reason - having it this weekend seems like too much of a rush. There is no need to rush you. Take the quiz. Learn from your mistakes.
- The test will open Friday, and close Tuesday.
- Thursday and Friday this week there is no new preparation. We will be working in small groups in class, using the ideas we've learned so far to explore the final topics of the semester.
- Monday is our review/lesson plan day. The instructions are in the problem set (at the end of chapter 5). Take all quizzes twice by that day, as I will be locking them all after that point.
- Tuesday the exam closes. Remember that the testing center closes during devotional, so plan accordingly.
- Consider the solid region in space below the paraboloid $z=9-x^2-y^2$ and above the $xy$-plane.
- Set up an integral using cylindrical coordinates to find the volume using the order $d\theta dz dr$. Compute the two inside integrals, till only one integral is left.
- Set up an integral using cylindrical coordinates to find the volume using the order $d\theta dr dz$. Compute the two inside integrals, till only one integral is left.
- One of the integrals above we call the shell method, the other we call the disc method. Which is which, and why?
- Set up an integral formula to compute each of the following average values:
- The average temperature of a metal plate in the $xy$-plane bounded by the curves $y=x$, $y=2$, and $x=0$, where the temperature at points on the plate is given by $T(x,y)=\sin(y^2)$.
- The average charge density on a wire that lies along the helix $\vec r(t) = (a\cos t,a\sin t, bt)$ for $0\leq t\leq 4\pi$, provided the charge at each point on the wire is given by $\rho(x,y,z) = xz$.
- The average pressure in a solid region in space that lies above the cone $z^2=4x^2+4y^2$ and below the paraboloid $z=9-x^2-y^2$, provided the pressure at each point is given by $p(x,y,z) = 10+x$.
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