Problem Calculating a limit with a square root, i'm stuck

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Homework Help Overview

The discussion revolves around calculating a limit involving a square root, specifically the limit of the expression (9-t) / (3-√t) as t approaches 9. Participants are exploring methods to simplify the expression to evaluate the limit.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the use of the conjugate to simplify the expression and question whether the limit exists based on their manipulations. Others suggest factoring the numerator as an alternative approach.

Discussion Status

The discussion is active, with differing opinions on the existence of the limit. Some participants are exploring the implications of their algebraic manipulations, while others are providing alternative strategies for simplification.

Contextual Notes

There is a focus on the algebraic manipulation of the limit expression, with participants questioning assumptions about the methods used and the nature of the limit itself.

Jordash
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Problem Calculating a limit with a square root, I'm stuck :(

Homework Statement




The limit is equation 9-t / 3-sqrt(t) as t approaches 9

I'm stuck on the how to simplify this?

Thanks for any help.


Homework Equations





The Attempt at a Solution

 
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Try multiplying by (3+√t)/(3+√t)
 


I discovered that that is the conjugate and I came out with this:

27-6sqrt(t)-tsqrt(t)
----------------
9-t

So in other words, that limit does not exist. Is that right?
 


The limit does exist. Instead of multiplying by the conjugate over itself, just factor the numerator, treating it as the difference of two squares.
 

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