In this example we look at proving a limit result by using the precise definition of a limit.
This definition often confuses people but really we are just trying to capture the notion of 'closeness' by using absolute value and inequalities.
This type of limit example where we deal with a linear function is largely mechanical, so even if you absolutely have no clue what the heck is really going on, you should be able to memorize the steps easily enough!
Note that the notion of a limit of crucially important in calculus.
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