Objectives: In this tutorial, we finally obtain the formal defintion of limits and relate this definition to our previous definition. We verify this definition for a few examples. First, we find algebraically the delta corresponding to a specific epsilon and then find algebraically the delta for an arbitrary epsilon.

Working through these materials, the student should be able to find algebraically the delta corresponding to a specific epsilon and then find algebraically the delta for an arbitrary epsilon.

Modules:

 Definition. The limit of f(x) as x approaches a is L if and only if, given e > 0, there exists d > 0 such that 0 < |x - a| < d implies that |f(x) - L| < e.

• Discussion of how to obtain the above formal definition of limits from our previous definition of limits.
[Using Flash]

• Examples of finding delta given a specific epsilon.

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• [Using Flash]

• Examples of finding delta for a general epsilon.

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• [Using Flash]

• Drill on finding d given a specific e.

• Drill on finding d given a general e.