Determine the infinite limit

[gr8joel]

The limit of ln((x^2)-9) as x approaches 3 from the right.

I have decided to make a table of values for x really close the the right side of 3. This is what I get:

f(3.1)=-0.494296321
f(3.01)=-2.811745437
f(3.001)=-5.115829157

Thus far it doesn't seem to be approaching any limiting value.

The answer in the back of my book says it's equal to negative infinite.

Can someone please help me jump start this problem so I can understand how to actually evaluate this infinite limit problem?
Thanks in advance

 

[tkhunny]

That is demonstrating divergence. It is not proving divergence. You didn't notice the negative absolute values increasing?

You may wish to factor the difference of squares in the argument, and separate the pieces to consider separately.

 

[JeffM]

Let u = x[sup:cramtqdu]2[/sup:cramtqdu] - 9.
What is the limit of u as x approaches 3 from the right.
So, is u greater or less than 1 when x is close to 3?
So, is ln(u) positive or negative?
So, is ln(u) bounded or not as u approaches its limit?