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From the intuitive notion of a limit, if

, then

can be made as close to

as desired simply by finding an

that is sufficiently close to

. The formalized version of this is the

definition of a limit. In this case

. Select a value for

and you can find a corresponding

so that, if

, then

Snapshot 1: Select an

Snapshot 2: Find a corresponding

Snapshot 3: Close in on the limit.

Contributed by: Joseph F. Kolacinski (Siena Heights University)

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A Case of the Epsilon-Delta Definition of a Limit