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