Mathematics 133 -- Calculus with Fundamentals 1

Exam 2 -- Things to Know

October 6, 2017

General Information

The second full-period exam of the semester will be given in class on Friday, October 20 (that's the week after October break). It will cover the material from sections 1 - 7 of Chapter 2 (basically since the last exam, through the material from Friday, October 6). There will be four or five questions (some with several parts) similar to problems from the quizzes, problem sets, and in-class practice problems so far. Graphing calculators will be allowed on this exam.

We will do some review for the exam in class on Thursday October 19, and Tori will run a review session for last-minute questions on the exam on Thursday evening, October 19 at the usual time (7 - 9pm).

Material To Know

You should know the following material.

• As you should have realized, a lot of the stuff from Chapter 1, especially things about piecewise-defined functions, operation on fuctions, various classes of functions, is relevant here too. The new material from Chapter 2 is:
• Section 2.1: Determining instantaneous velocities by limits of average velocities, and slopes of tangent lines by limits of slopes of secant lines. (You should recognize that the limits we need there are examples of the indeterminate forms we saw later in Section 2.5.)
• Section 2.2: The idea of limits, estimating limits numerically and graphically. (Even though we know better methods now, you should still be able to use these approaches to understand what the limits mean intuitively.)
• Section 2.3: The Limit Laws (Sum, Product, Quotient, Powers and Roots)
• Section 2.4: Continuity -- be able to recognize continuity or discontinuities graphically using one-sided limits, and be able to show a function is continuous at a given x = c by applying the Limit Laws
• Section 2.5: Indeterminate form limits (especially 0/0 and infinity/infinity forms), algebraic techniques or evaluating these limits.
• Section 2.6: The Limit Squeeze Theorem, the limit lim_{x -> 0} sin(x)/x = 1.
• Section 2.7: Recognizing vertical asymptotes from formulas for functions, limits as x -> +/- infinity and horizontal asymptotes.

Good Review Problems:

There is an extensive section of Chapter 2 Review Problems in the text. I suggest you try the odd numbered problems on paper, then check your answers. (You can omit problems 69-80, though, since we did not cover Sections 2.8 and 2.9.)

Also see the sample exam questions posted on the course homepage.