Indeterminate Limits
A Limit does not Exist
When you first try the plug-in technique and discover that the answer is
some number (except zero) divided by 0 (undefined) then the limit does
not exist.
Note:
0
2
is indeterminate, while
is undefined.
0
0
Exam
Continuity
As with limits, continuity is a very important mathematical concept to
understand. Many of the subsequent theorems, definitions and
conjectures in calculus will depend on the principle of continuity.
In defining the limit lim f x
xo a
L , we ha
Limits Involving Infinity
The symbol for infinity, , does not represent a real number. We use
i
nf
i
ni
t
yt
odescr
i
bet
hebehavi
ourwhent
hef
unct
i
on
sDomain or Range
becomes very large. We are usually interested in the value of f when x
become extrem
Rates of Change and Tangent Lines
The Average Rate of Change of a quantity over a period of time is the
amount of change divided by the change of time.
y
We say, Average Rate of change
where x is the independent
x
variable and y is the dependent variable
The Concept of a Limit
The concept of the limit of a function is one of the most fundamental ideas
that distinguishes Calculus from the other disciplines of mathematics such
as Geometry and algebra. It is in the understanding of this concept that
will bin