Two Variable Limit: Solve xy²/(sin(x²+y²))

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Homework Help Overview

The problem involves evaluating the limit of the expression (xy²)/(sin(x² + y²) as (x,y) approaches (0,0). The original poster expresses uncertainty about how to handle the sine function in the denominator and considers using Taylor series, questioning its applicability in a multivariable context.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • One participant suggests switching to polar coordinates as a potential method for simplifying the limit evaluation. The original poster's attempt at a solution indicates a belief that the limit may be 0, but they seek clarification on the approach to take regarding the sine function.

Discussion Status

The discussion is ongoing, with participants exploring different methods and clarifying the original poster's thought process. There is no explicit consensus on the best approach, and some participants emphasize the importance of showing effort before receiving assistance.

Contextual Notes

There are reminders about forum rules regarding assistance with homework problems, highlighting the expectation for participants to demonstrate their attempts before receiving help. This context may influence the nature of the responses and guidance offered.

Anoonumos
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Hi,

Homework Statement



lim (xy²)/(sin(x² + y²))
(x,y) -> (0,0)

The Attempt at a Solution


I think the answer is 0, but I don't know how to get rid of the sin (x² + y²). I thought about using taylor series but I'm not sure if that works with two variables.

Can someone help me out?
 
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How about switching to polar coordinates?

r^2 = x^2 + y^2
 
sunjin09 said:
Mod note: help removed[/color]

Maybe someone can justify the tilde somehow ...

I suggest you read this:

https://www.physicsforums.com/showthread.php?t=414380

"On helping with questions: Any and all assistance given to homework assignments or textbook style exercises should be given only after the questioner has shown some effort in solving the problem. If no attempt is made then the questioner should be asked to provide one before any assistance is given. Under no circumstances should complete solutions be provided to a questioner, whether or not an attempt has been made.
"
 
Last edited by a moderator:
I think I've solved it.
(xy²)/(sin(x² + y²) = (x² + y²)/(sin(x² + y²) * (xy²/(x²+y²))
And I know both these limits (1 and 0).
 
deleted
 
Last edited:
DivisionByZro said:
I suggest you read this:

https://www.physicsforums.com/showthread.php?t=414380

"On helping with questions: Any and all assistance given to homework assignments or textbook style exercises should be given only after the questioner has shown some effort in solving the problem. If no attempt is made then the questioner should be asked to provide one before any assistance is given. Under no circumstances should complete solutions be provided to a questioner, whether or not an attempt has been made.
"

sunjin09 said:
I thought his only problem was how to get rid of the sine, which I didn't help with, only helped clarifying his thought in a form that facilitates thinking.

BTW, giving an answer directly is still better than no answer at all, I'll be glad to take any answer to my questions, which more often than not go unanswered.
@sunjin09

By now I see that a PF Moderator has removed your offending post.

DivisionByZro was merely pointing out to you some of the rules for posting help on this Forum.

It's your opinion that "... giving an answer directly is still better than no answer at all, ...", but if you continue to try to exercise that behavior in this Forum, I suspect that the Moderators will take your privileges to post.
 
Last edited:

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