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

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Homework Help Overview

The discussion revolves around evaluating the limit of the expression (X³ + 3X²)/(X² + 6X + 9) as X approaches -3. Participants are exploring the implications of reaching an indeterminate form during the limit evaluation.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the calculations leading to the limit, questioning the results and interpretations of the forms encountered, particularly the transition from a numerical result to the concept of limits not existing.

Discussion Status

The conversation reflects a progression through confusion regarding the calculations, with some participants clarifying their understanding of the indeterminate form 0/0 and its implications for the limit's existence. Guidance has been offered in the form of corrections to calculations and conceptual clarifications.

Contextual Notes

Participants are navigating the complexities of limit evaluation, particularly in the context of indeterminate forms, and are reflecting on their assumptions about the behavior of the function as X approaches -3.

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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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