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

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SUMMARY

The limit of the function (X³ + 3X²)/(X² + 6X + 9) as X approaches -3 is determined to be DNE (Does Not Exist). The initial confusion arose from the calculation yielding 0/0, which is an indeterminate form. Upon further analysis, it was clarified that the denominator approaches 0 while the numerator also approaches 0, confirming the limit does not exist. This discussion highlights the importance of recognizing indeterminate forms in limit evaluations.

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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.
 
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How are you getting -18 on the bottom?
 
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?
 
0/0 is an indeterminate form, so it's still possible for the limit not to exist.
 
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 :)
 

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