Objectives: The following is a list of theorems that can be used to evaluate many limits. After working through these materials, the student should know these basic theorems and how to apply them to evaluate limits.

Modules:

Theorem A. Suppose that f and g are functions such that f(x) = g(x) for all x in some open interval interval containing a except possibly for a, then

• Discussion of Theorem A [Using Flash]

  Theorem B. Suppose that f and g are functions such that the two limits exist, suppose that k is a constant and suppose that n is a positive integer. Then [Example] [Example] [Example] [Discussion using Flash] [Example] [Discussion using Flash] [Example] [Discussion using Flash] [Example] [Example] [Example] [Example] [Example] [Example] [Example] [Discussion using Flash] [Example] [Discussion using Flash]

  Theorem C. The limit if and only if the right-hand limits and left-hand limits exist and are equal to M:

• Examples:
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     [Discussion using Flash]

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  Theorem D. (Squeeze Theorem) Suppose that f, g and h are three functions such that f(x) < g(x) < h(x) for all x. If then

• Example:
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     [Discussion using Flash]

  Theorem E. Suppose that f and g are two functions such that then the limit does not exist.

• Example:
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     Discussion [Using Flash]