Precise Definition of a Limit - Example 1

in MES Science2 months ago (edited)

In this video I go over a very useful example to illustrate the precise definition of a limit which I went over in my last video. This is a tricky subject to understand but it is very important to understand fully so make sure to watch this video!


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Precise Definition of a Limit – Example 1

Precise Definition of a Limit  Example 1.jpg

Precise Definition

Let f be a function defined on some open interval that contains the number ‘a’, except possibly at ‘a’ itself.

Then we can say that the limit of f(x) as x approaches ‘a’ is ‘L’, and we write:

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If for every number ε > 0 there is a number δ > 0 such that:

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Example

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Solution

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NOTE

The graphical procedure given above gives an illustration of the definition for ε = 0.2 but it does NOT prove that the limit is 2.

A proof has to provide a δ for every ε.

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