Mathematics 135 -- Calculus 1

Exam 2 -- Things to Know

October 10, 2016

General Information

The second full-period exam of the semester will be given in class on Friday, October 28 (that's the second week after October break). It will cover the material from sections 1 - 7 of Chapter 2, and sections 1 - 2 of Chapter 3 (Problem Sets 3,4,5, or basically since the last exam, through the material from Wednesday October 19). There will be four or five questions (maybe with several parts) similar to problems from the quizzes, problem sets, and in-class practice problems so far. Graphing calculators will not be allowed on this exam.

I will be happy run a review session for the exam on Wednesday evening, October 26. (Thursday is not good for me this time because of a Montserrat CHQ cluster event.)

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 Chapters 2,3 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.
• Section 3.1: The limit definition of the derivative of a function; computing derivatives by the definition
• Section 3.2: The derivative as a function

Good Review Problems:

See the Chapter Review Problems for Chapter 2, p. 110 - 111 in the text, and the sample exam questions posted on the course homepage.