The final exam is cumulative, that is, it covers all the material from the first day of class onwards. Approximately 50-60% will cover the material from Chapters 4 and 5. This is sections 14.1 - 14.5 and 15.1 - 15.6. You should go over homework problems, class notes and past quizzes and exams.

The exam will be designed for 100 minutes (twice the length of the mid semester exams) so you should have plenty of time to complete it in the alloted 2.5 hour time slot. You will be expected to use a calculator on the exam. However, you are not allowed to store formulas in your calculator's memory nor use any graphing capabilities your calculator may have for curve sketching problems.

**FINAL EXAM Review:** Thursday, Dec. 6th, in SWORDS 359 from 1:00 - 3:00 pm. Please come prepared
with specific questions from the chapter reviews, past exams, homework problems, etc.

** List of Topics By Chapter **

- Chapter 1: Precalculus review (laws of exponents, simplifying expressions, factoring, solving equations), Cartesian coordinates, quadratic formula, distance formula, absolute value, equation of a circle, equation of a line, slope of a line
- Chapter 2: Functions, domain and range of a function, graphing functions, algebra of functions (adding, subtracting, etc.), composition of functions, types of functions (constant, polynomial, rational, square root, etc.), limits (left-sided, right-sided), limits as x approaches + or - infinity, continuity (know the three conditions in order for a function to be continuous at a point), the derivative (know the limit definition as well as a geometric understanding of the derivative), calculating derivatives using the difference quotient, non-differentiable functions (absolute value, cusps)
- Chapter 3: Rules of differentiation --- power rule, product rule, quotient rule, chain rule, marginal functions in economics (cost, average cost, revenue, profit, marginal cost, marginal revenue, etc.), higher-order derivatives, implicit differentiation
- Chapter 4: Using the derivative to describe properties of a function (increasing, decreasing, relative maxima, relative minima, concavity, inflection points), vertical and horizontal asymptotes, curve sketching, absolute max's and min's, optimizing a function (word problems)
- Chapter 5: Exponential functions, the number e and its importance, logarithmic functions, the natural logarithm ln x and its relation to e^x, graphs of exponential and logarithmic functions, properties of exponentials, properties of logs, compound interest (compounded annually, semi-annually, quarterly, ... , compounded continuously), derivatives of exponential functions and logarithmic functions, exponential growth or decay (word problems), half-life of a radioactive substance

Some sample problems from Chapter 4 and 5 are given below. Note that this is only a partial list. In many cases, the homework problems more accurately reflect the material covered in class. For example, there are better word problems from the homework in Section 4.5 than there are in the Chapter 4 review. For problems from the other Chapters, see the review sheets from past Exams and quizzes.

**Chapter 4 review, pp. 369-371**

Problems: 1, 9, 13, 17, 19, 25, 29, 38

**Chapter 5 review, pp. 437**

Problems: 1, 4, 8, 13, 19, 23, 27, 29, 33, 39, 41, 43, 46

**Note:** The answer to problem 4 is 15/2. The answer to problem
8 is y + 2z. The answer to problem 46 is 970 students.