## Math 122 - Final Exam Study Guide

1. The graph of y' is shown. Determine if the function is one-to-one on the interval shown.
2. Find dy/dx for functions involving natural logarithms, exponential, and inverse trigonometric functions. Three parts.
3. Use L'Hopital's rule to find the limits. Two parts.
4. Evaluate the integrals involving hyperbolic functions. Know the formulas for the inverse hyperbolic trig functions. Two parts.
5. Match the differential equation to the direction field. Three parts.
6. Solve the differential equation. Two parts. One is separable, one needs the integrating factor.
7. Tell whether the series converges (absolutely), converges conditionally, or diverges. You don't need to identify the test used Eight parts.
8. Find a Maclaurin series for a function.
9. Find the integral of a series.
10. Find the derivative of a series.
11. Transform the equation into polar form.
12. Transform the equation into rectangular form.
13. Sketch the curve in polar coordinates. Two parts.
14. Find the area in polar coordinates.
15. Use integration by parts to evaluate the integral.
16. Use trigonometric substitution to evaluate the integral.
17. Use partial fractions to evaluate the integral.
18. Evaluate the improper integral.
19. Show that the sequence is eventually strictly increasing or strictly decreasing.
20. Find the sum of a series. Pay attention to geometric series and telescoping series.
21. Evaluate the integral involving trigonometric functions.
22. Identify each statement as true or false. Fifteen parts. Concentrate on properties of hyperbolic trig functions, integration by parts, exponential and logistic growth models, convergence and divergence of tests, monotonic series, convergence of a power series, derivatives of a power series, partial fraction decomposition with repeated or irreducible quadratic factors, the relationship between the derivatives of trig functions and their cofunctions, the relationship between the derivatives of hyperbolic trig functions and their reciprocal functions, the convergence of a p-series, the convergence of a finite series.

### Notes:

• The final exam is open notebook.
• You may copy tables from the book and put in your notebook. In particular, make sure you get the derivatives and integrals of trig, inverse trig, hyperbolic trig, and inverse hyperbolic trig functions.
• Make sure this study guide is in your notebook, along with any notes about where to find information.
• If there are any areas of the test where your notes are weak, supplement them before taking the exam.
• You may begin the exam early if you want to; I will be in the room beginning at 5:30.
• There is a 50 point take home portion of the final exam. It is due at the beginning of class on the day of the final.
 # 1 2 3 4 5 6 7 8 9 10 11 Pts 2 12 8 10 6 10 16 5 5 5 4 # 12 13 14 15 16 17 18 19 20 21 22 Total Pts 4 8 5 5 5 5 5 5 5 5 15 150