1.2 The Concept of a Limit
Definition (not rigorous):
Consider a function
f
and a number
c
that has a neigh
borhood where
f
is defined (though
f
need not be defined at
c
itself).
c
c
c
1. The
limit of
f
(
x
)
as
x
goes to
c
from below (or from the left)
, lim
x
→
c

f
(
x
),
is that number that the outputs of
f
get closer and closer to as the inputs
increase and get closer and closer to
c
.
If the outputs of
f
aren’t getting
close to any number then we say that this limit
does not exist
or is
undefined
.
If the outputs of
f
are positive and get huger and huger then formally the
limit is undefined but to describe why it is undefined we say that the limit is
‘equal to’ +
∞
. If the outputs of
f
are negative and get huger and huger (in
absolute value) then again the limit is formally undefined but we say that it
is ‘equal to’
∞
in order to describe why it is undefined.
2. The
limit of
f
(
x
)
as
x
goes to
c
from above (or from the right)
, lim
x
→
c
+
f
(
x
),
is defined in exactly the same way as the limit of
f
(
x
) as
x
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '07
 Vorel
 Calculus, Limits, Limit, Continuous function

Click to edit the document details