Approaching 0: Rationalizing the Limit x→4 √x-4

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Homework Help Overview

The discussion revolves around evaluating the limit as x approaches 4 for the expression √x - 4. Participants are exploring the implications of substituting the value directly into the expression and the resulting undefined or zero outcomes.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the challenges of directly substituting the limit value, noting that it leads to an undefined result. There is mention of rationalizing the expression and using conjugates, as well as considerations of proving the limit using epsilon-delta definitions.

Discussion Status

The conversation is ongoing, with participants questioning the necessity of certain mathematical techniques and the validity of their approaches. There is no explicit consensus on the best method to proceed, but various strategies are being considered.

Contextual Notes

Some participants express concern about obtaining a zero result and question the appropriateness of direct substitution in this context. The discussion includes references to specific mathematical concepts like conjugates and epsilon-delta proofs, indicating a focus on foundational understanding.

heythere1010
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Homework Statement


lim x→4 √x-4
I need to do something so that it is not undefined or 0.

Homework Equations

The Attempt at a Solution


I tried rationalizing, but that just gave me x-4/√x+4, which would still result in an undefined answer.
 
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What exactly is the problem?
 
PeroK said:
What exactly is the problem?
If I sub in 4 from the beginning, I will get sqrt 0. I can't have that as my answer.
 
heythere1010 said:
If I sub in 4 from the beginning, I will get sqrt 0. I can't have that as my answer.
Why not?
 
PeroK said:
Why not?
I thought you would need to do something like conjugates for it.
 
Not unless you have to prove it from first principles using epsilon-delta.
 

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