# Math 122 - Chapter 11 Study Guide

1. Write the polar equation of the graphed relation. Six parts.
2. Transform the polar equation into rectangular coordinates. Look at problems 11.1.9-10.
3. Express the given rectangular equation in polar form. Look at problems 11.1.11-12.
4. Find dy/dx at the given point without eliminating the parameter. Look at problems 11.2.5-10.
5. Calculate the arclength of a polar curve. Look at problems 11.2.39-44. Set up the integral, but do not evaluate it.
6. Find the area of the region described in polar form. Look at problems 11.3.3-20.
7. Solve the initial value problem.
8. Find the general solution to the second order differential equation with constant coefficients.
9. Find the sum of the infinite series.
10. Find the general term of the sequence, determine if the sequence converges and if so, to what.
11. Find the radius of convergence and the interval of convergence.
12. Find a Maclaurin series for the expression.
13. Find a polar equation for the conic section that is described. Look at problems 11.6.5-8, 13-14.
14. Identify each series as absolutely convergent, conditionally convergent, or divergent. Five parts. You do not need to show work or identify the test used.
15. For the conic section given in polar form, identify the eccentricity and the conic, describe the distance and relationship of the pole to the directrix, find the coordinates of the vertices (or vertex), and sketch the graph. Look at problems 11.6.1-4, 9-12.
16. Use Simpson's method to approximate the area under a curve.
17. Sketch the ellipse and label the foci, vertices, and endpoints of the minor axis. Look at problems 11.4.9-14.
18. Sketch the hyperbola, and label the vertices, foci, and asymptotes. Look at problems 11.4.15-20.
19. A slope field is given along with an initial condition. Sketch the solution curve.
20. Integrate using integration by parts.
21. Integrate using a trigonometric substitution.
22. Evaluate the improper integral.
23. Integrate the trigonometric integral.

## Notes

• The in-class part of the test is worth 158 points.
• There is a take home portion of the exam. The take home portion is worth 42 points and is due on the day of the exam.
• Handout on Conic Sections. This has all of the information about conics in rectangular coordinates, but it is a fill-in-the-blank activity for students to take notes.
• Summary sheet for conic sections in rectangular coordinates. This has just the facts, but it's not fill-in-the-blank
• You will need WinPlot to generate the graphs for the last question on the take home exam.
• There is a page to help with the LORAN-C problem on the take home.
• You may use the front and back of an 8.5"×11" sheet of paper for notes to use during the exam. This sheet must be handwritten and will be collected with the exam.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Total 18 6 6 6 6 6 6 6 5 5 6 6 6 15 6 5 10 10 4 5 5 5 5 158