# How do you prove the statement lim as x approaches 4 for #(7 – 3x) = -5# using the epsilon and delta definition?

##### 1 Answer

See the explanation section below.

#### Explanation:

**Our preliminary work**

We need to show that, given any positive

Let's look at the thing we need to make less than

# = abs(12-3x)#

Because we say how to find

Not that if we factor out a

# = abs(-3)abs(x-4) = 3abs(x-4)#

We have found that

If we make

Now we need to present ourwokr as a proof.

**Proof**

Given

# = 3abs(x-4) < 3 delta = 3(epsilon/3) = epsilon.# .

That is,

**Note that **

near the middle we used, without mention, the fact that