The final exam is CUMULATIVE, that is, it covers all the material from the first day of class onwards. Approximately 15-20% will cover material from Chapter 11. This is Sections 11.1, 11.2, 11.4 and 11.5. You should go over homework problems as well as your class notes. Many of the problems and questions we discuss in class are excellent examples of test questions.

I have listed some sample problems from the Chapter 11 Review and Check Your Understanding sections below. For review questions from other chapters, see the three previous exam review sheets. For Ch. 6, 7.1 - 7.4, see Exam 1 . For Sections 7.5 - 7.8, 8.1 - 8.4, 8.7 and 8.8, see Exam 2 . For Chs. 9 and 10, see Exam 3 . It is also a good idea to go over your previous exams (solutions available from the course webpage.) The exam will be designed to take two hours although you will have the full 3 hours.

Click here for **some practice questions** (PDF file)
for the exam. You should ignore questions 7, 13 and 18b as these test material we
did not cover. Solutions are available ** here** (PDF file).

**Note:** You will be allowed one "cheat sheet" 8.5 x 11 piece of paper, front and back, full of whatever formulas,
graphs, etc. you wish. You will be given a scientific calculator for the exam which does NOT have graphing
capabilities so be prepared to answer questions without your personal calculator or computer. The only
numerical computations required will be the kind a scientific calculator can perform.

**Exam Review:** We will review for the exam Thursday, May 11, 12:30 - 2:00 pm
in Swords 359. Please come prepared with specific questions.

** List of Topics By Chapter **

- Chapter 6: Antiderivatives (graphically, analytically and numerically), 1st and 2nd Fundamental Theorems of Calculus, equations of motion
- Chapter 7: Integration: u-substitution, by parts, using a table, partial fractions, trig. substitution. Approximating integrals: left, right, midpoint, trapezoid, Simpson's rule, comparison of methods and error, improper integrals
- Chapter 8: Applications of the definite integral: areas, volumes, volumes of solids of revolution, polar coordinates (area, graphing, converting to and from Cartesian coordinates), density, center of mass, distribution functions, probability, mean and median
- Chapter 9: Series: geometric (finite and infinite), convergence or divergence of an infinite series. Tests for convergence: n-th term test, integral test, comparison test, ratio test, alternating series test. Power series: radius of convergence, interval of convergence
- Chapter 10: Approximating functions: Taylor polynomials, Taylor series, finding a Taylor series using a known series, using Taylor series to approximate functions, error in a Taylor polynomial approximation
- Chapter 11: Differential equations: Testing a possible solution to an ODE, slope fields, separate and integrate, finding the solution to an initial-value problem, growth and decay (exponential model, Newton's law of cooling)

**Chapter 11 review, pp. 595 - 598**

Problems: 1, 3, 5, 7, 9, 15, 19, 21, 29, 31a, 35

**Chapter 11 "Check Your Understanding", pp. 599 - 600**

Problems: 4, 5, 6, 8, 9, 11, 12, 25, 26

The answers to the evens are:

4. FALSE (What if y = 0?)

8. FALSE

12. FALSE (Try finding the second derivative of a solution.)

26. TRUE