How can I solve this limit algebraically without using the conjugate method?

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Homework Help Overview

The discussion revolves around evaluating the limit of the expression (x^.5 - x^2)/(1 - x^.5) as x approaches 1. Participants explore various algebraic methods to solve the limit without using the conjugate method.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss attempts to manipulate the expression through techniques such as long division and factoring. Questions arise about the effectiveness of these methods and the reasoning behind certain algebraic manipulations.

Discussion Status

The conversation is ongoing, with participants sharing different approaches and questioning the validity of each other's methods. Some guidance has been offered regarding long division and factoring, but no consensus has been reached on the best approach to take.

Contextual Notes

There are indications of confusion regarding the algebraic steps and the implications of certain transformations. Participants express uncertainty about how to handle the remainder from long division and the significance of specific algebraic identities in the context of the limit.

  • #31
I can't read the jpeg for some reason, but I also got 3 by decomposing the numerator in the original equation (x^0.5-x^2) = x^0.5(1-(x^0.5)^3) which is a cubic and can be further factored as x^0.5(1-x^0.5)(1+x^0.5+x). The (1-x^0.5) cancel out leaving x^0.5)(1+x^0.5+x). Then take this limit as x goes to 1 gives 3. I imagine that's similar to what wurth did
 

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