Help with Limit Homework Problem - Simplifying

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Homework Help Overview

The discussion revolves around a limit problem involving the expression \(\lim_{x\to 0}\frac{\frac{1}{3+x}-\frac{1}{3}}{x}\). Participants are exploring methods to simplify this limit and identify any potential errors in their approaches.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to simplify the limit using a conjugate but expresses uncertainty about the effectiveness of this method. Other participants suggest starting with simplification of the fractions involved and combining terms with a common denominator.

Discussion Status

Participants are actively discussing different approaches to simplify the limit expression. Some guidance has been offered regarding the simplification process, and there is acknowledgment of potential errors in earlier attempts. The conversation indicates a productive exploration of the problem without reaching a definitive conclusion.

Contextual Notes

The original poster mentions a previous attempt that led to confusion, indicating possible math errors in their calculations. There is an emphasis on ensuring correct simplification steps are followed.

crybllrd
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Homework Statement



I'm having trouble with a homework problem:

[tex]\lim_{x\to 0}\frac{\frac{1}{3+x}-\frac{1}{3}}{x}[/tex]

I wasn't sure how to simplify this. I tried a conjugate, but assuming I did it right, it didn't get me anywhere.
 
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Hi crybllrd! :smile:

You may start by simplifying

[tex]\frac{1}{3+x}-\frac{1}{3}[/tex]...
 
crybllrd said:

Homework Statement



I'm having trouble with a homework problem:

[tex]\lim_{x\to 0}\frac{\frac{1}{3+x}-\frac{1}{3}}{x}[/tex]

I wasn't sure how to simplify this. I tried a conjugate, but assuming I did it right, it didn't get me anywhere.

[tex]\lim_{x\to 0}{\frac{1}{3x+x^2}-\frac{1}{3x}}[/tex]

Then combine terms with a common denominator.

You'll see it after that.
 
Thanks guys, I was making that way more difficult than it was.
I had done it the right way the first time, but I guess I made a math error because it didn't work out. I did it correctly now, though.
Thanks again!
 

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