# Basic Limit Laws

Listed here are a couple of basic limits and the standard limit
laws
which, when used in conjunction, can find most limits. They are listed for
standard, two-sided limits, but they work for all forms of limits. However,
note that if a limit is infinite, then the limit does *not* exist.

## Basic Limits

If *c* is a constant, then
.

.

## Limit Laws

If the limits
and
both exist,
then

.

If the limits
and
both exist,
then

.

If *c* is a constant, and the limit
exists, then

.

If the limits

and

both exist,
then

.

If the limits
and
both exist,
and
,
then

.

If *n* is an integer, and the limit
exists, then

.

If *n* is an integer, the limit
exists,
and that limit is positive if *n* is even, then

.

If
for all *x* in an open interval that contains *a*, except possibly
at *a* itself, and
,
then

.

If *f* is continuous at *b* and
,
then

.

Copyright © 1996 Department
of Mathematics, Oregon State University
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