# How do you prove limit of #14-5x=4# as #x->2# using the precise definition of a limit?

##### 1 Answer

Using

Let

Thus:

Algebraically, this makes sense; yet we want to prove this using the precise definition of a limit.

Since the general formula looks like:

This implies that:

This means that as we pick an interval on the x-axis that is close to

So, if we plug in the values we know:

We want to manipulate

so that it can represent

Now they look similar and we can see that

**This gives us a ratio for when you're given a distance from #L# (or an error tolerance).**

So, lets choose

That concludes our proof.