# Precise Definition of a Limit - Example 2: Proving Limits Exist

in MES Science2 months ago (edited)

In this video, I go further into the precise definition of a limit and do an example on proving that the limit of 4x-5 as x approaches 3 is equal to 7. This is a very useful video because I illustrate how you can easily rearrange some functions in such a way so that you can easily apply the precise definition of a limit in proving them.

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# Precise Definition of a Limit – Example 2

## 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:

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

## Example 2

### Solution

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