I'm getting 2 different values for this limit but am i doing it right/

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Homework Help Overview

The discussion revolves around evaluating a limit in a multivariable context, specifically examining the behavior of a function as the variables approach a point in three-dimensional space.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to evaluate the limit by approaching the point (0,0,0) along different paths, leading to two different limit values. Participants question the parameterization used in one of the approaches.

Discussion Status

Participants are exploring the implications of obtaining different limits from different approaches and discussing the conditions under which a limit exists. There is an acknowledgment of the need for consistent parameterization in evaluating the limit.

Contextual Notes

The original poster mentions fixing one variable while varying the others, which raises questions about the assumptions made in the limit evaluation process.

mr_coffee
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Hello everyone, I'm having troubles deciding if this limit does not exist...
i have the problem and work here, i get 2 different limits by letting x and y go to different points and making z fixed at 0. Did i break any rules?

http://img426.imageshack.us/img426/1372/lastscan7fk.jpg
 
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You forgot to indicate your parameterization in the second attempt. What was it?
 
It seems to have been (t,t,0).
 
correct (t,t,0)
 
Yes, in order for the limit to exist, f(x,y,z) must be close to that limit when (x,y,z) are close to 0, no matter how you approach (0,0,0). Since you get two different limits approaching along two different lines, this limit does not exist.
 

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