Mathematics 133 -- Calculus with Fundamentals 1
Exam 3 -- Things to Know
November 3, 2017
General Information
The third full-period exam of the semester will be given
in class on Friday, November 10. It will cover the
material from sections 1 - 7 of Chapter 3 (basically since the last exam, through
the material from Monday, November 3). 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 be allowed on this exam, but using the graphing
capabilities will not be needed on any of the questions.
Tori will run a review session for the
exam on Thursday evening, November 9.
Material To Know
You should know the following material.
- As you will have realized, almost all of the stuff from Chapters 1 and 2, especially
things about piecewise-defined functions, operation on fuctions, various classes
of functions, all of our techniques for computing limits, continuity, etc. is
relevant here too. The new material from Chapter 3 is:
- Section 3.1: The definition of the derivative as the limit of the difference
quotient, computing derivatives from the limit definition. Be prepared to do one
of these calculations. This will involve one of the three types of indeterminate
form limits we concentrated on in Section 2.5.
- Section 3.2: The derivative as a function, the shortcut rules for sums, constant
multiples, powers
xn, and the exponential function ex; the
connection between the graphs y = f(x) and y = f '(x) (what it
means for f '(x) to be positive or negative on an interval, what it means for
f '(a) = 0 for some a, etc.)
- Section 3.3: The Product and Quotient Rules for derivatives. Know the
statements of both well and be able to use them separately and in combinations.
- Section 3.4: There will not be as much emphasis on this section as the others,
but you should recognize that if a question asks for an instantaneous rate of
change of some quantity, then mathematically, it is asking for the derivative
of that quantity with respect to whatever variable is specified.
- Section 3.5: Higher derivatives. Be able to compute any of these. (The rules
are exactly the same as in 3.1, 3.3, etc. because, for instance, f '' = (f')'.)
- Section 3.6: Derivatives of trigonometric functions. Know the derivative
rules in Theorems 1 and 2 from this section, and be able to apply them in combination
with the other rules from 3.1, 3.2, 3.3, etc.
- Section 3.7: The Chain Rule (for derivatives of compositions) -- Know what it
says and how to apply it in combination with the other rules from 3.1, 3.2, 3.3, 3.6.
(Note: This will be covered in class on Friday, 11/3.)
- The material on implicit differentiation from Monday, 11/6 will not be covered
on this exam.
Good Review Problems:
The Chapter 3 Review Problems
from our book (with answers for the odd-numbered problems).
I suggest you try the odd numbered problems on paper, then check your answers.
(You can omit the problems numbered 101 and higher for now; we have not studied
that material yet. There are also a number of those problems that require you
to differentiate functions such as the natural logarithm or the inverse
trigonometric functions. We haven't discussed the derivative formulas for
those yet, so you will not be responsible for knowing them. )
Also see the sample exam questions posted on the course homepage.