What Is the Limit of (2-x)/(x^2-4) as x Approaches 2?

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Homework Help Overview

The discussion revolves around finding the limit of the expression (2-x)/(x^2-4) as x approaches 2, a topic within calculus focused on limits and continuity.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to find the limit using substitution and factoring, questioning the next steps after factoring the denominator. Some participants introduce the concept of limits and suggest alternative approaches, including l'Hospital's rule.

Discussion Status

Participants are exploring various methods to approach the limit, with some providing insights into limit laws and others suggesting techniques like l'Hospital's rule. There is an ongoing exploration of the problem without a clear consensus on the best method.

Contextual Notes

The original poster notes that the substitution method was unsuccessful, indicating potential complexities in the limit evaluation. The discussion includes references to specific mathematical laws and rules applicable to limits.

screamtrumpet
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lim (2-x)/(x^2-4)
x>2

Find the limit(is it exists)

The substitution method failed so I factored the bottomto (x+2)(x-2).Where do I go from here?
 
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A very important but often overlooked "law of limits":

If f(x)= g(x) for all x except x= a, then [itex]\displaytype\lim_{x\to a}f(x)= \lim_{x\to a} g(x)[/itex].

Here, for all x except x= 2, (2- x)/(x-2)(x+2)= -1/(x+2).
 
use l'Hospital's rule
 
Thank you
 

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