Pre-Class Lesson 3
Today, wont you join us for a discussion on FUNCTION OPERATIONS?
To start, lets recall that we have 4 basic operations of arithmetic addition,
subtraction, multiplication, and division. Just as we can do these operations with
numbers, v
Pre-Class Lesson 4
How about we jump right in and talk about LINEAR FUNCTIONS AND MODELS?
Do you know what we mean when we say MODEL? Were going to be using that term a lot this
semester. Basically a MODEL is a way to explain or represent observations. In
Pre-Class Lesson 6
Now, settle in for a moment, because we have a LOT of definitions and terminology to go
over. Are you ready? Here we go
A POLYNOMIAL FUNCTION can be represented by
() = + 1 1 + + 2 2 + 1 + 0
Where each coefficient is a real number, does
Pre-Class Lesson 1
Hi again! Good to see we didnt scare you away last time. Hopefully by now you
have registered on MyLabsPlus and maybe begun your first homework assignment.
If not, you need to do that ASAP before you fall too far behind.
Now last time w
Pre-Class Lesson 2
Hey there everybody! Welcome back! Were going to spend pretty much the
entire rest of the semester talking about, looking at, describing, solving, and
generally manipulating all kinds of different FUNCTIONS. This lesson is an
overview o
Pre-Class Lesson 0
Hello and Welcome to College Algebra (1203/1204) at the University of Arkansas. Over the
next 5 or 8 or 16 weeks, you will learn, explore, apply, problem solve, discuss, and
communicate mathematical topics. If you have taken High School
U NIVERSITY OF A RKANSAS
D EPARTMENT OF M ATHEMATICS
Calculus 1 Drill
Section 5.4 Working with Integrals
Todd Thomas
26 November 2013
1 I NTEGRATING E VEN AND O DD F UNCTIONS
Symmetry appears throughout mathematics in many different forms, and its use oft
( MATH 2554 EXAM 1 25 September, 2013 NAME(PRINT):
You must show your work. You must give ID#
Complete justications for your conclusions Drill Inst & Time:
Otherwise, N0 CREDIT!
3x24x4
1) Evaluate: Lim
x+2 x2
2
, . _ . x +3x10
2) Write the equat10ns of al
U NIVERSITY OF A RKANSAS
D EPARTMENT OF M ATHEMATICS
Calculus 1 Drill : Section 4.6 Mean Value
Theorem
Todd Thomas
January 7, 2014
The Mean Value Theorem is a cornerstone in the theoretical framework of calculus. Several
critical theorems rely on the Mean
U NIVERSITY OF A RKANSAS
D EPARTMENT OF M ATHEMATICS
Calculus 1 Drill : Section 4.5 Linear
Approximation and Differentials
Todd Thomas
December 9, 2013
Imagine plotting a smooth curve and pick a point on the curve P . Now draw the line tangent to the curv
U NIVERSITY OF A RKANSAS
D EPARTMENT OF M ATHEMATICS
Calculus 1 Drill : Section 4.8 Antiderivatives
Todd Thomas
18 November 2013
1 A NTIDERIVATIVES
The goal of differentiation is to find the derivative f 0 of a given function f . The reverse operation, ca
U NIVERSITY OF A RKANSAS
D EPARTMENT OF M ATHEMATICS
Calculus 1 Drill
Section 5.5 Substitution Rules
Todd Thomas
26 November 2013
1 I NDEFINITE I NTEGRALS
One way to find new Antiderivative rules is to start with familiar derivative rules and world backwa
U NIVERSITY OF A RKANSAS
D EPARTMENT OF M ATHEMATICS
Calculus 1 Drill : Section 4.7 L Hopitals Rule
Todd Thomas
12 November 2013
We have studied many limits, but some limits still cannot be solved using the techniques that
we have learned. These limits ar
Definition 1 Limit of a Function: Assume that f (x) exists for all x in some
open interval containing a, except possibly at a. We say that the limit of f (x)
as x approaches a is L.
Remark 2 Steps for proving that lim f (x) = L
xa
1. Find . Let be an arbi
Math 2554 Quiz 5.35.5 Name 023w 7W." 4 Zcq
Show your work clearly.
Find the area of the shaded region. 3
1) g 7? 709. Mg
/\ (3)1313 , new
2 i, 3
)3 lg, r2-2/r
\ - - V Eff . EH 23
2) Find the averagevalue off(x)=cosxon [-n/2,n/2]. AT 3 E 5
TV? 72 (h/
U NIVERSITY OF A RKANSAS
D EPARTMENT OF M ATHEMATICS
Calculus 1 Drill
Section 5.2 Fundamental Theorem of Calculus
Todd Thomas
21 November 2013
1 F UNDAMENTAL T HEOREM OF C ALCULUS
A REA F UNCTIONS The concept of an area function is critical to the discuss
U NIVERSITY OF A RKANSAS
D EPARTMENT OF M ATHEMATICS
Calculus 1 Drill
Section 5.1 Approximating Areas Under Curves
Todd Thomas
21 November 2013
1 S ECTION 5.1 T HE D EFINITE I NTEGRAL
We use Riemann sums to partition and then approximate the area under a
MATH 2564C 8.2 LIMITS OF SEQUENCES
PAOLO MANTERO
8.1 & 8.2 Limits of Sequences
Last time we have seen that a sequence is a collection of number (with index n running through the natural
numbers). Today we start studying these objects by introducing some
MATH 2564C 9.1 9.3 TAYLOR POLYNOMIALS AND TAYLOR SERIES
PAOLO MANTERO
Section 9.1: Taylor Polynomials
If f (x) is a function and x = a is a point (e.g. a = 0, or a = 1, etc.), then we can approximate f (x) in several
ways, for instance
the linear approx
MATH 2564C 8.4 THE DIVERGENCE AND INTEGRAL TESTS
PAOLO MANTERO
Recall: In the last classes we have seen
Pthe following.
A series is an infinite sum. A series n=1 an is just
X
an = lim sn
n
n=1
where sn is the sequence of the sum of the first n terms (be
MATH 2564 C 7.0 REVIEW OF INTEGRATION
PAOLO MANTERO
Anti-derivatives
A function F (x) is an anti-derivative of f (x) if f (x) is the derivative of F (x)
(i.e. if F 0 (x) = f (x). For instance, 2x is the derivative of x2 , hence x2 is an
anti-derivative o
MATH 2564C 9.2 PART 1 POWER SERIES
PAOLO MANTERO
Recall: Last time we have seen the last Tests for Series (Root Test and Ratio Test), that we now recall as we
are going to need them a lot today.
Theorem 1 (The Ratio Test). Let an be a sequence.
P
an is a
MATH 2564C 8.2 SPECIAL LIMITS AND ALTERNATING SEQUENCES
PAOLO MANTERO
Example 1. Does the sequence an = cos(n) converge? If yes, to what number?
Sol. Note that
n
= cos().
n
n
It is not clear what is cos() (it could be any number between 1 and 1.). So to