Mathematics 133 -- Calculus with Fundamentals 1
Exam 2 -- Things to Know
October 7, 2015
General Information
The second full-period exam of the semester will be given
in class on Thursday, October 22 (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 9). There will be eight or nine questions
(maybe grouped together as parts of larger
questions) similar to problems from the quizzes, problem sets, and in-class practice problems
so far.
Graphing calculators will not be allowed on this exam.
Lauren will run a review session for the
exam on Wednesday evening, October 21.
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 limx -> 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 online e-book version of the Chapter 1 Review Problems
from our book posted on LaunchPad (with answers for the odd-numbered problems).
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.