Limit in Two Variables: Approaching the 0/0 Case

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Homework Help Overview

The discussion revolves around evaluating a limit in two variables that results in an indeterminate form of 0/0. Participants are exploring different approaches to determine the existence of the limit.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants suggest examining the limit from different paths approaching (0,0) to see if different limits are obtained, which would indicate that the limit does not exist. There are discussions about substituting specific functions like y=x and y=x^3 to analyze the limit's behavior.

Discussion Status

The conversation is ongoing, with participants sharing their attempts at evaluating the limit and questioning the validity of their approaches. Some have noted that they are getting consistent results while others are exploring various substitutions to check for discrepancies.

Contextual Notes

There is an emphasis on the need to find different limits through various paths to conclude about the limit's existence. Participants are also considering the implications of using specific substitutions in their evaluations.

tysonk
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How do I approach such question,
0/0 case in two variables, I can't find a simplification.

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Thanks for the help.
 
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Look for two ways to approach (0,0) that will give you different limits. That will prove the limit doesn't exist and you don't have to worry about it anymore.
 
isn't it -1?

edit: oh got it

2nd edit: nope still got -1

I approached from both possible y's
 
veneficus5 said:
isn't it -1?

edit: oh got it

2nd edit: nope still got -1

I approached from both possible y's

Look at the limit as y->0 when x=0 and the limit as x->0 when y=0.
 
I learned that one can plug in things like y=x, y=2x to help determine whether a limit can exist. If a different value is obtained then a limit may not exist.
Is it still possible to plug in y=x^3

Because when we plug in y=x and y=x^3 we get different values. Thanks.
 
tysonk said:
I learned that one can plug in things like y=x, y=2x to help determine whether a limit can exist. If a different value is obtained then a limit may not exist.
Is it still possible to plug in y=x^3

Because when we plug in y=x and y=x^3 we get different values. Thanks.

Sure. That works. I still think x=0 and y=0 are easier, but it's your choice.
 

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