Amitoj Singh
MA160
Jacobowitz
Homework Review
1. Is defined
Find )
Is continuous
Is differentiable at this value of?
for this value
(limxfax
at this value
()fx x
of x? If so ()fx if it exists.
of? ()fx x
estimate . ()fa
a=4
3
3
Yes
Yes
a=5
Not defined
Doe
Victor Omokehinde
Period 7
Pythagoras of Samos
Pythagoras was a Greek philosopher, mathematician, and founder of the
movement called Pythagoreanism. He is often referred as the first pure mathematician.
He was born on the island of Samos, Greece in 569 BC
1
Functions and Models
1.5
Exponential Functions
Exponential Functions
The function f (x) = 2x is called an exponential function
because the variable, x, is the exponent. It should not be
confused with the power function g(x) = x2, in which the
variable i
1
Functions and Models
1.1 Four Ways to Represent a Functio
Four Ways to Represent a Function
Functions arise whenever one quantity depends on another.
Consider the following four situations.
A. The area A of a circle depends on the radius r of the
circle
1
Functions and Models
1.6
Inverse Functions and Logarith
Inverse Functions and Logarithms
Table 1 gives data from an experiment in which a bacteria
culture started with 100 bacteria in a limited nutrient
medium; the size of the bacteria population was re
1
Functions and Models
1.2
Mathematical Models:
A Catalog of Essential Functions
Mathematical Models: A Catalog of Essential Functions
A mathematical model is a mathematical description (often
by means of a function or an equation) of a real-world
phenome
1
Functions and Models
1.4
Graphing Calculators and Compu
Graphing Calculators and Computers
Graphing calculators and computers can give very accurate
graphs of functions.
A graphing calculator or computer displays a rectangular
portion of the graph of a
1
Functions and Models
1.3New Functions from Old Function
Transformations of Functions
3
Transformations of Functions
By applying certain transformations to the graph of a given
function we can obtain the graphs of certain related
functions.
This will giv
1
Functions and Models
1.7
Parametric Curves
Parametric Curves
Imagine that a particle moves along the curve C shown in
Figure 1.
Figure 1
It is impossible to describe C by an equation of the form
y = f (x) because C fails the Vertical Line Test. But the
Amitoj Singh
MA160
Jacobowitz
Practice Problem Sets
1. The graph of the
Find )(limxfax
function is shown.
if it exists.
Use this graph to
answer the questions
in the chart below.
()fxIs defined for
this value of x? If so
()fx
estimate . ()fa
a=4
a=5
a=6
a
Amitoj Singh
MA160
Jacobowitz
Study Guide
Optimization in Business and Economics
Marginal and average cost
As in a previous chapter, Cost function C(q) is the cost of
producing q units
Average cost c(q) =
The absolute minimum of the average cost, c, could
Amitoj Singh
MA160
Jacobowitz
Stude Guide
Review 1
1.1 Functions and Their Representations
Intro to functions
A function is a mathematical relationship in which one quantity
is determined by another.
worlds
graph of
earthquake.
Examples - A formula like t