Converting Sin to Absolute Value for Multi-Variable Limits

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Homework Help Overview

The discussion revolves around finding the limit of the expression sin(x^2+y^2)/(x^2+y^2) as (x, y) approaches (0, 0). The problem is situated within the context of multivariable calculus and limit evaluation.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply the squeeze theorem and questions how to convert sin(x^2+y^2) into an absolute value format. Some participants suggest considering polar coordinates as an alternative approach.

Discussion Status

Participants are exploring different methods for evaluating the limit, with some suggesting the conversion to polar coordinates as a potentially more effective strategy. There is no explicit consensus on the best approach yet.

Contextual Notes

The original poster is considering the use of inequalities and the squeeze theorem, indicating a focus on rigor in the limit evaluation process. There may be assumptions about the behavior of the sine function near zero that are under discussion.

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Homework Statement


Find the limit for x = 0 y= 0 for sin(x^2+y^2)/x^2+y^2


Homework Equations



I'm trying to use the squeeze method using the inequality |ab| <= 1/2(a^2+b^2)


The Attempt at a Solution



Is there a way I can convert sin(x^2+y^2) into absolute value |ab|

so I can get |ab| <= (1/2(x^2+y^2))/x^2+y^2


or should I use a different inequality?
 
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I don't think the approach you're attempting will do you any good. How about converting to polar coordinates? Then you're looking at the limit as r approaches zero.
 
Hi,

should I find the limit r -> 0 of sin(R^2)/R^2

= 1

regards
 
That's what it looks like to me.
 
Thanks a lot!
 

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