Calculating the Limit for sqrt(x^2-9)

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Homework Help Overview

The discussion revolves around calculating the limit of the expression sqrt(x^2-9) as x approaches 3. Participants are exploring the implications of the limit and the behavior of the function near this point.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the evaluation of the limit and question whether the limit is 0 or undefined. There is also inquiry into the requirements for a limit to exist, particularly focusing on the behavior of the function as it approaches the limit from both sides.

Discussion Status

Some participants have provided guidance regarding the conditions under which a limit exists, noting that the limit must approach the same value from both sides. There is an ongoing exploration of the implications of the function's behavior near the limit.

Contextual Notes

There is a mention of the function never actually reaching 0, which raises questions about the nature of limits and continuity at that point.

moberry
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Homework Statement



lim sqrt(x^2-9)
x->3


Homework Equations



I understand that the radical will evaluate to 0. I am not sure if the answer to the limit is 0, or undefined


The Attempt at a Solution



lim sqrt((3)^2-9) = sqrt(9-9) sqrt(0) = 0
x->3


Thanks for your help.
 
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What is the requirements for a limit to exists?
 
Hootenanny said:
What is the requirements for a limit to exists?

The limit coming from both sides, must approach the same y-value. In this case 0. The function will never hit 0, but will get infinitely close. That would make the value of the limit 0??
 
moberry said:
The limit coming from both sides, must approach the same y-value. In this case 0. The function will never hit 0, but will get infinitely close. That would make the value of the limit 0??
Correct :approve:
 
Hootenanny said:
Correct :approve:

Good deal. I thought that was it. Wanted to be 100% sure.
 

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