key term - Algebraic Manipulation

Definition

Algebraic manipulation refers to the process of using mathematical operations such as factoring, simplifying, and manipulating algebraic expressions to determine the limit of a function. It involves rearranging and manipulating equations to find alternate forms that make it easier to evaluate the limit.

Related terms

Limits:

Limits are mathematical tools used to describe what happens when we approach a particular value or point on a graph. They help us understand how functions behave near certain points.

Continuity:

Continuity refers to whether or not there are any breaks, holes, or jumps in the graph of a function. It is closely related to limits because limits play a role in determining if a function is continuous at a given point.

Indeterminate Forms:

Indeterminate forms are expressions that cannot be evaluated using straightforward substitution. These often occur when trying to find limits involving fractions with zero denominators or when dealing with infinity. Special techniques such as algebraic manipulation may be needed to evaluate these types of limits.