Indeterminant limit (radical in denominator)

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Homework Help Overview

The discussion centers on evaluating the limit of a rational expression as \( x \) approaches 4, specifically involving a radical in the denominator. The expression under consideration is \( \lim_{x \to {4}}\frac{4 - x^2}{2 - \sqrt{x}} \).

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the manipulation of the expression to evaluate the limit, with one participant attempting to simplify the expression by multiplying by a conjugate. Questions arise regarding the correctness of the expansion and whether the limit is indeterminate at the specified point.

Discussion Status

There is an ongoing exploration of the algebraic manipulation involved in the limit evaluation. Some participants have pointed out potential errors in the expansion of the numerator, while others have acknowledged corrections made to the initial attempts.

Contextual Notes

Participants are addressing the indeterminate form of the limit and the implications of the algebraic steps taken. The discussion reflects a focus on ensuring accurate representation of the expressions involved.

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Homework Statement



[tex]\lim_{x \to {4}}\frac{4 - x^2}{2 - \sqrt{x}}[/tex]

Homework Equations


The Attempt at a Solution



[tex]\lim_{x \to {4}}\frac{4 - x^2}{2 - \sqrt{x}} \cdot \frac{2 + \sqrt{x}}{2 + \sqrt{x}}[/tex]

[tex]= \frac{x(4-x)(2-\sqrt{x})}{(4-x)} = x(2-\sqrt{x})[/tex]

this equals zero, but is the limit indeterminate at this point?
 
Last edited:
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I think you expanded the numerator incorrectly
 
thanks! it was a missed minus sign.
 
4-x^2 = (2-x)*(2+x)
 

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