# 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

### Addition Law

If the limits and both exist, then

.

### Subtraction Law

If the limits and both exist, then

.

### Constant Law

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

.

If the limits

and

both exist, then

.

### Division Law

If the limits and both exist, and , then

.

### Power Law

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

.

### Root Law

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

.

### Squeeze Law

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

.

### Composition Law

If f is continuous at b and , then

.

Copyright © 1996 Department of Mathematics, Oregon State University

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