# How do you prove the statement lim as x approaches -1.5 for # ((9-4x^2)/(3+2x))=6# using the epsilon and delta definition?

##### 2 Answers

You can't.

#### Explanation:

You can't prove it since it isn't 6.

See the explanation.

#### Explanation:

**Preliminary analysis**

We need to show that for every positive

Note first that

For every

So, for every

# = abs(-2x-3) = abs((-4)(x+3/2)) = abs(-4)abs(x+3/2)# .

# = 4abs(x+3/2)#

We want this to be less than

If we make

Now we are ready to write the proof:

**Proof**

Given

Now if

# = abs(-2x-3) = abs(-4)abs(x+3/2)# .

# = 4abs(x+3/2) < 4delta = 4(epsilon/4) = epsilon#

That is: if

So, by the definition of limit,