Math 122: Chapter 10 Exam Study Guide

1. Write the polar equation of the graphed relation. These could involve roses, lemniscates, limaçons, cardiods, circles, ellipses, hyperbolas, and parabolas. (9 parts)
2. Given a parametrically defined curve.
   1. Find dy/dx and d²y/dx²
   2. Find the slope and concavity at the indicated point.
   3. Find the equation of the line tangent to the curve at the indicated point.
3. Convert the rectangular equation into polar form. Solve for r. (4 parts)
4. Convert the polar equation into rectangular form. (4 parts)
5. Find the rectangular equation of the described parabola.
6. You are given a parametrically defined curve on an interval.
1. Eliminate the parameter to write the equation in rectangular form. Pay attention to any restrictions on the variables.
2. Find the length of the curve.
3. Find the area of the surface when the curve is rotated around a coordinate axis.
4. Find the area of the surface when the curve is rotated around a line (not a coordinate axis).
7. You are given an equation in polar form.
   1. Find the derivative dy/dx.
   2. Find the length of the curve.
   3. Find the area enclosed by the curve.
   4. Find the area of the surfaced generated when a portion of the curve is rotated about the polar axis.
   5. Find the area of the surfaced generated when a portion of the curve is rotated about the θ = π/2 axis.
8. The eqations for two polar curves are given.
   1. Find the area between the curves.
   2. Find the area between the loops of a limaçon.
9. A polar equation for a conic section is given.
   1. Find the eccentricity and identify the graph as a parabola, ellipse, or hyperbola.
   2. Find the distance from the pole to the directrix and describe the relationship of the directrix to the pole.
   3. Find the vertex or vertices.
10. Find the rectangular equation of the described hyperbola.
11. Find the rectangular equation of the described ellipse.
12. Find the polar equation for the described conic with a focus at the pole. (2 parts)

Notes

• For problems requiring integration, first write the appropriate integral and then use the numeric integration feature of your calculator to approximate the value.
• There is a take home exam worth 50 points. It is due the day of the regular exam.
• There is a page to help with the LORAN-C problem on the take home.
• There are 110 possible points, which means that you can miss 10 points without hurting your grade.
• You should bring paper for work. Write your answers on the exam itself.

Points per problem

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Last updated May 5, 2011 5:55 AM