92.131
Lecture 9
1 of 8
Ronald Brent © 2009 All rights reserved.
One-Sided Limits
Definitions:
Right-Hand Limit
L
x
f
a
x
=
+
→
)
(
lim
means that
L
x
f
→
)
(
as
a
x
→
from the right.
That is
a
x
→
, and
a
x
>
.
Left-Hand Limit
L
x
f
a
x
=
−
→
)
(
lim
means that
L
x
f
→
)
(
as
a
x
→
from the left.
That is
a
x
→
, and
a
x
<
.
The ordinary limit exists iff both the left and right hand limits exist and are
equal.
L
x
f
a
x
=
→
)
(
lim
⇔
L
x
f
a
x
=
−
→
)
(
lim
AND
L
x
f
a
x
=
+
→
)
(
lim

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