MAC2313, Calculus III
Exam 2 Review
Exam 2 covers the materials from lectures 114. This review is not designed
to be comprehensive, but to be representative of the topics covered on the
exam.
1. Let ~
MAC2313, Calculus III
Exam 1 Review
This review is not designed to be comprehensive, but to be representative
of the topics covered on the exam. You may also pick up an old MAC2313
exam at Broward Tea
Lecture 2: Calculating Limits Using the
Limit Laws (Section 2.3)
Limit Laws
Suppose lim f (x) and lim g(x) exist and c is a
x!a
x!a
constant. We have the following limit laws:
1. lim [ f (x) g(x) ] =
Lecture 5: Derivatives and Rates of Change
(Section 2.7)
Velocity
Suppose an object moves along a straight line
according to an equation of motion s = f (t) where s
is the displacement from the starti
Lecture 7: Derivatives of Polynomials and
Exponential Functions (Section 3.1)
In Lecture 5 we defined the derivative of a function
in terms of a limit and have so far used that definition in our examp
Lecture 4: Limits at Infinity; Horizontal
Asymptotes (Section 2.6)
x2
Consider the graph of f (x) = 2
:
x +1
6

?
What happens to the values of f (x) as x increases to
positive infinity or as x decre
Lecture 8: The Product and Quotient Rules
(Section 3.2)
In this lecture we introduce two new rules which will
aid us in dierentiating the product or quotients of
functions.
ex. Let f (x) = x2 and g(x)
Lecture 3: Continuity (Section 2.5)
Def. A function f is continuous at a number a if
lim f (x) = f (a). If f is defined on an open interval
x!a
including x = a but is not continuous there, then f
is d
Lecture 6: The Derivative as a Function
(Section 2.8)
In the previous lecture we defined the derivative of a
function f at x = a to be
f 0(a) =
if the limit exists.
For each new value of a, a separate
Def. For a function f (x), we say that lim f (x) = L
x!a
if the values of f (x) get closer and closer to L as the
values of x get closer and closer to a.
x if x 6= 1
ex. If f (x) =
, find lim f (x).
Lecture 4: Techniques for Integration
II. part II: Evaluate Integrals of tanm x secn x
Recall
(tan x)0 = sec2 x
(sec x)0 = sec x tan x
1 + tan2 x = sec2 x
Z
tan x dx = ln  sec x+c = ln  cos x+c
Z
Module 9: Guided Notes
2.6 Graphs of Basic Functions (pages 248252)
Definitions
Continuity: a function is continuous over an interval of its domain if its hand drawn graph over that
interval can be s
Module 5: Guided Notes
1.1 Linear Equations (pages 8891)
Definitions:
Equation: a statement that two expressions are equal.
Solution: all the numbers that make the equation a true statement
Linear Eq
Module 2: Guided Notes
1.3 Complex Numbers (pages 105111)
Definitions
i = square root 1
i 2 = 1
a + bi = if a and be are real numbers then this is a complex number, a is the real part and b
is the
Module 8: Guided Notes
1.7 Inequalities (pages 150158)
Inequalities and their Graphs
1. Read page 150. What is the one way in which solving inequalities is different from solving
equalities? Click on
Module 1: Guided Notes
R.2 Real Numbers and Their Properties (pages 915)
Fill in the chart of Real Numbers from page 10, then answer questions about the chart.
Real Numbers = the set of all numbers t
Module 6: Guided Notes
1.4 Quadratic Equations (pages 113120)
Definitions
Quadratic Equation: an equation that can be written in the form ax^2 + bx + c = 0 where a, b and c are
real numbers with a no
Module 3: Guided Notes
R.3 Polynomials (pages 2430)
Rules for Exponents
Fill out the chart below. For the examples, create ones that are different from those in the book.
Operation
Multiplying
m
n
a
Module 7: Guided Notes
1.6 Other Types of Equations and Applications (pages 136145)
Rational Equations
Solve the equations below. The equation on the left is a review from M5 while the equation on th
Module 10: Guided Notes
2.6 Graphs of Piecewise and Greatest Integer Functions (pages 253255)
Piecewise
1. Define a general piecewise function. (What makes something piecewise? What makes
something a
Module 4: Guided Notes
R.6 Rational Exponents (pages 5560)
Rules for Exponents (expanded)
Fill out the chart below. For the examples, create ones that are different from those in the book.
Operation
Module 4: Guided Notes
R.6 Rational Exponents (pages 5560)
Rules for Exponents (expanded)
Fill out the chart below. For the examples, create ones that are different from those in the book.
Operation
Module 1: Guided Notes
R.2 Real Numbers and Their Properties (pages 915)
Fill in the chart of Real Numbers from page 10, then answer questions about the chart.
4
Rational Numbers
_
5
9
Irrational Nu
Module 3: Guided Notes
R.3 Polynomials (pages 2430)
Rules for Exponents
Fill out the chart below. For the examples, create ones that are different from those in the book.
Operation
Multiplying
=
Exa
71.1"59 Paw/in
Module 5: Guided Notes
1.1 Linear Equations (pages 8891)
/
SfMUrhMl mew rvvo expressiovm M2 eqv
"mar nnoung w cfw_M Wu mm an quaw we
mm
For eadI,provideadenition(inyourownwmds)an
MAC 2311 Test 2A
1. What is the equation of the tangent line to the graph of
f (x) = 2x3 4x2 + 3x 1 at the point (1, 0)?
A. y = 2x 2
B. y = 2x + 2
C. y = x + 1
D. y = x 1
E. y = 3x 3
2, x a
, for whi