The Rectangular Coordinate System
def: The Cartesian coordinate system is 2 number lines put together, with positive x-values to the right,
positive y-values up.
To plot a point/ordered pair (a, b) , go a _, and b _, and draw in the point as
1.1 Real Numbers
def: The set of _ numbers is cfw_1, 2, 3, 4,
def: The set of _ numbers is cfw_0, 1, 2, 3,
def: The set of _ is cfw_., 3, 2, 1,0,1, 2,3,.
def: Set-builder notation is cfw_x x has some property
e.g. Rewrite the set
a. cfw_x x is
To solve a formula for a specified variable, isolate that variable on one side of the equation.
Note: You may still clear fractions from the equation.
e.g. Solve V r 2 h for h
e.g. Solve j
d for a
e.g. Solve R
1.6: Algebraic Expressions
def: A variable is a symbol used to represent a number.
def: An (algebraic) expression consists of numbers, variables, operation symbols and grouping symbols.
Expressions do not contain _
def: An _ is a statement that t
Solving Linear Equations, 1-Step Problems
def: A linear equation in one variable is an equation that can be written Ax B 0 for real A,B and A 0.
def: A solution to an equation is _
e.g. Is 5 a solution of 3x 2 13 ?
e.g. Is 7 a solution of 4
1.3 Exponents & Order of Operations
def: x n x x
x is called the _ of the exponent.
_ of them
n is the _ or the _.
Order of Operations:
Please: _. Work inside grouping symbols, from the inside out.
D = rt
Motion and Mixture Word Problems
e.g. A car averages 63 mph for 3 hours. How far did the car travel?
For distance chart problems, you may need to draw a picture.
e.g. Label a variable, set up an equation, and solve.
Which line below would you like to represent your salary over the next several years? Why?
def: The slope of a line is a measure of the direction a line goes and how steep it is.
positive slope means the line goes _ as it goes to the r
Chapter 13 Worksheet
Section 13.1 Area Under a Curve
A special notation exists that uses the Greek letter
(capital sigma) to express the
sum of numbers or expressions. This notation is called sigma notation.
We may indicat
Chapter 9 Worksheet
Section 9.1 Limits
A Geometric Example of Limit:
Lets look at a polygon inscribed in a circle. If we increase the number of sides of the
polygon, what can you say about the polygon with respect to the circle?
Chapter 10 Worksheet
Section 10.1 Relative Maxima and Minima: Curve Sketching
The first derivative identifies the turning points of the graph of a function. Turning
points are points at which the graph changes direction (that is, changes
Chapter 11 Worksheet
Section 11.1 Derivatives of Logarithmic Functions
Definition of the Base-b Logarithmic Function
Let b 0 and b 1. The logarithmic function
y log b x
has domain x 0, base b, and is defined by
Chapter 12 Worksheet
Section 12.1 Indefinite Integrals
We have studied procedures for finding derivatives of functions. We will now turn our
attention to reversing this process of differentiation. When we know the derivative of a
Chapter 14 Worksheet
Section 14.1 Functions of Two or More Variables
We write z f x, y to state that z is a function of both x and y. The variables x and y
are called the independent variables and z is called the dependent variable. Thus
Math 1100 Final Review
1.7 Exponents and Order of Operations
Evaluate each expression
Pg. 66 46) 18 6 3
58) 14 + 3(7 5 3)
84 ) (3 5 2 6)4
1.8 Algebraic Expressions
Pg. 76 Write an algebraic expression for each.
32) 21 less than the total height h.
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Section 3.1 Quadratic Functions
* Graph as Parabolas (Section 2.5)
y a x h k
f ( x) ax 2 bx c
If a > 0, then the parabola opens
If a < 0, then the parabola
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A rule or correspondence that assigns to each member of one set
and only one member of a second set
A function has 3 main parts
How do we know if a rela
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f ( x) b x
b 0, b 1, x
is a real number
If b 1 ,
If 0 b 1 ,
Exponential Growth and Exponential
f ( x
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Exam #4 Practice, Ch. 4 and 5.1-5.5
REMEMBER THIS IS A SAMPLING OF EXAM #4 PROBLEMS.
BE SURE TO DO THE HOMEWORK TO GET ALL POSSIBLE PROBLEMS.
1. Given: y 4 x 1 1
Consider the work done on an object moving in a force eld F along the curve C: rm = x'trj + y(;j + nk .
Work = [Force)cfw_ J! Hum L3 1
so we only have to consider the part ofthe 'force parallel to the direction of movement.
u (E '1- 1: (t)
def: Flux is the voiurneiof uid crossing a surface per unit of time.
def: Let Fcfw_x. Jae = M i + N j + Pk , where M, N. Phave continuous rst partial derivanVes on S. oriented h; N.
ThenxintegralofFaerossSis HF-Nt. rt;-
5 Poilh tn
Note: If p is the
"M L <PLNLE91JKEZ 1 (0&0? _
I Thenrcm: lfM. N. Fhavc unntinunus rst paniai den' valivas in an wen graham Q in space. then
the matte-r eld foty] = Mi + N] T
1]: is cunsmavc if'and uni: if Th: F = ii
VXFj Judansthat FIE:-
LEE an; an;
Footox Fonos ofGreonE Th
Consider a 1motor eld in rhe plane: Flu-Lu = Mi +N j _ "' 4 M J N >
Wnle B as a veetor eld 111 space _F: " <7 m N I C 2
1- Fi'nd eurlF. 7- V N cfw_3 bit
_ a. a.
- (3?)?3231)? <M'ND>
e E 4 '12 ._,.
F 9 L o~ ec
15.7: Divergence Theorem
When you evaluate surface integrals for a solid, you must use all surfaces of the solid.
e.g. Let Q be the solid between the xy-plane and z 9 x 2 y 2 , let S be the outer surface of that solid, and
let F( x, y, z) y, xy,
Ex A position function is s(t) = ~l6t2 + 65f for a projectile,
launched straight up from ground level. I ._
If(~e): 5(t)- 325. +6.5
0 Determine the velocity 5 ( l\ 3 32 ('5 + 55.
one second aer launch. 1f
1' 3 3 cfw_/554
Ex Determine the exact x-value f
Mixed Review for Final Exam
Ex Evaluate the limit
- lim 4tan(%x) Dy?
. x22x15 an: .
0 11m 2
2_ A _ 7c:
. limx 22X15:,Z,_ (7t 3yha> '3
x>w-3 x 9 _._ 3'.) 5'
2-3 (Xx-3) :3: /3
- lim ZxS - i
- Detennine the value of li
Test 3 Practice Problem
Consider the function
10 20 x
( 20 points )
a. Graph the function. Choose an appropriate scale for
the each axis. Be accurate.
b. What are the equations of the asymptotes, if any, of
the graph of the function?
c. Find coo
Test 1 In-Class Practice
lim 4 x 1
Find the number such that
f x L
f x L
4 x 1 3 0.03
4 x 2 0.03
2. Evaluate each limit statement Use
1. Use implicit differentiation to find
3 y 2 x 5 y 2 x 3
2. Use implicit differentiation to find
tan x sin 2 y
3. Consider the ellipse
x 2 4 y 2 16
. Find the equation for a line
that is normal to th