The final exam is CUMULATIVE, that is, it covers all the material from the first day of class onwards. Approximately 17-20% will cover material from Chapter 11. This is sections 11.1 - 11.4. 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 below. For questions from other chapters, see previous exam review sheets. (Ch. 6, 7.1, 7.2 -> Exam 1, Ch. 7, 8.1, 8.2 -> Exam 2, 8.3, 8.4, Chs. 9 and 10 -> Exam 3.) To give you some good conceptual questions to work on, I have listed some sample problems from the Chapter 8, 9, 10 and 11 "Check Your Understanding" sections. It is also a good idea to go over your previous exams. The exam will be designed to take two hours although you will have the full 3 hours.

**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 Sunday, May 4, 7:00 - 8:30 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, easy differential equations
- Chapter 7: Integration: u-substitution, by parts, using a table, partial fractions, trig. identities. 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, density, center of mass, work, gravity
- 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
- Chapter 10: Approximating functions: Taylor polynomials, Taylor series, finding a Taylor series using a known series, using Taylor series to calculate limits or approximate functions
- Chapter 11: Differential equations: Testing a solution to an ODE, slope fields, Euler's method, separate and integrate, finding the solution to an initial-value problem, synthesizing the techniques to obtain a complete picture of the ODE

**Chapter 8 "Check Your Understanding", pp. 401**

Problems: 1, 5, 8, 9, 12, 13, 23

The answers to the evens are:

8. FALSE

12. FALSE

**Chapter 9 "Check Your Understanding", pp. 431**

Problems: 6, 7, 11, 22, 23, 24

The answers to the evens are:

6. FALSE

22. TRUE

23. FALSE

24. FALSE

**Chapter 10 "Check Your Understanding", pp. 473-474**

Problems: 1, 3, 5, 8, 9, 13, 19

The answers to the evens are:

8. TRUE

**Chapter 11 review, pp. 552-553**

Problems: 3, 5, 9, 11, 15, 19, 31, 35

**Note: ** For #35, the set up is dy/dt = k(350-y)
where y(t) is the temperature of the roast at time t
measured in hours. Solve the differential equation
first and then use the information given to find k.
Finally, calculate the time when the roast reaches
a temperature of 140.

**Chapter 11 "Check Your Understanding", pp. 555-556**

Problems: 3, 5, 8, 9, 34, 37

The answers to the evens are:

8. FALSE

34. dy/dx = f(x), with f(x) a positive, increasing, differentiable function