What is the limit of (X³ + 3X²)/(X² + 6X + 9) as X approaches -3?

[chelceyd]

Homework Statement

Evaluate each limit. If the limit does not exist, so indicate.

lim as X approaches -3 of (X³+3X²)/(X²+6X+9)

Homework Equations

n/a

The Attempt at a Solution

I know that the answer is supposed to be DNE, but everytime I try to calculate it, I can't get the answer to not exist...I think I may just be looking at it wrong. I keep getting 0/-18.

 

[vela]

How are you getting -18 on the bottom?

 

[chelceyd]

Oh I forgot that (-3)² is positive 9, not negative 9. ok, so now I got 0/0. But isn't it supposed to be something like x/0? so that it is a DNE?

 

[vela]

0/0 is an indeterminate form, so it's still possible for the limit not to exist.

 

[chelceyd]

Ahhh ok, I got a little mixed up. I kept going with the equation and I got the DNE answer. Thank you so much for your help :) I just could not wrap my brain around this one :)