Mathematics 135 -- Calculus 1

Exam 2 -- Things to Know

October 22, 2019

General Information

The second full-period exam of the semester will be given in class on Friday, November 1. The new material will come from sections 4 - 7 of Chapter 2, and sections 1 - 4 of Chapter 3 (Problem Sets 3,4,5, plus the material from Friday, October 25). 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. You may use a graphing calculator on this exam.

Material To Know

You should know the following material.

• As you should have realized, a lot of the stuff from Chapter 1 and the beginning of Chapter 2, especially operation on fuctions, various classes of functions, the meaning of limits, the limit laws, is relevant here too. The new material from Chapters 2,3 is:
• 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 (know how to relate the graphs y = f(x) and y = f '(x)
• The derivative rules for f(x) = xⁿ and f(x) = e^x.
• Section 3.3: The product and quotient rules for derivatives. You'll need to memorize these to use them without having to think too hard about how they work. Also know the proof of the product rule. Be able to apply these to examples like the ones from problem set 5 and the daily worksheets.
• Section 3.4: The chain rule for derivatives. Know what it says for a general composition f(g(x)) (i.e. memorize the statement of the rule) and know how to apply it to particular derivative computations.

Good Review Problems:

See the Chapter Review Problems for Chapter 2, p. 110 - 111 and Chapter 3, p. 189 - 191, problems 1 - 44 in the text (you're not responsible for derivative problems involving trig or inverse trig functions because we have not learned those yet). Also see the sample exam questions posted on the course homepage.