Math 1314
Lesson 2
OneSided Limits and Continuity
OneSided Limits
Sometimes we are only interested in the behavior of a function when we look from one
side and not from the other.
Example 1
:
Consider the function
x
x
x
f
=
)
(
.
Find
).
(
lim
0
x
f
x
→
Now suppose we are
only
interested in looking at the values of
x
that are bigger than 0.
In this case, we are looking at a
onesided limit
.
We write
)
(
lim
0
x
f
x
+
→
.
This is called a righthand limit, because we are looking at values
on the right side of the target number.
In this case,
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentIf we are interested in looking only at the values of
x
that are smaller than 0, then we
would be finding the lefthand limit.
The values of
x
that are smaller than 0 are to the left
of 0 on the number line, hence the name.
We write
)
(
lim
0
x
f
x

→
.
In this case,
Our definition of a limit from the last lesson is consistent with this information.
We say
that
L
x
f
a
x
=
→
)
(
lim
, if and only if the function approaches the same value,
L
, from both the
left side and the right side of the target number. This idea is formalized in this theorem:
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 MARKS
 Continuity, Limits, Continuous function

Click to edit the document details