Find the limit, of severable variables

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Homework Help Overview

The discussion revolves around finding the limit of a function as the variables (x, y) approach (0, 0). The function involves a combination of polynomial terms in both x and y.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to evaluate the limit by substituting specific values for x and y, questioning the validity of concluding that the limit is zero based on these substitutions.

Discussion Status

Participants are engaging in a back-and-forth about the evaluation of the limit, with one participant pointing out a potential simplification of the expression. There is an acknowledgment of the need for further exploration of the limit's behavior.

Contextual Notes

There is a mention of seeking additional practice problems, indicating a desire for further learning resources related to this type of limit evaluation.

th3plan
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Homework Statement



limit as (x,y)---->(0,0)
x^3 +xy^2/(x^2 + y^2)




The Attempt at a Solution



i tried letting x = 0, and get zero, and i also let , y= 0 and got 0, and then i let y=x , and got , zero, how can i be sure sure this limit is zero? What do i do ?

Thanks
 
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th3plan said:
limit as (x,y)---->(0,0)
x^3 +xy^2/(x^2 + y^2)

Hi th3plan! :smile:

You have noticed that this is x(x^2 +y^2)/(x^2 + y^2) ?
 
ohh duhh, as always not being observent. Good catch, do you any sites that have practice problems similar to this ?

Thanks
 
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