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

In summary, a two variable limit is a mathematical concept that involves finding the limit of a function with two variables as they approach a specific point or value. To solve a two variable limit, one must determine the approach direction and use algebraic manipulation or substitution techniques. The purpose of solving a two variable limit is to better understand the behavior of a function and make predictions. Some common examples include finding the limit at 0 or infinity, or at a specific point. Tips for solving two variable limits include identifying the approach direction, simplifying the function, using substitution or L'Hopital's rule, and visualizing the function with a graph.
  • #1
Anoonumos
16
0
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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  • #2
How about switching to polar coordinates?

r^2 = x^2 + y^2
 
  • #3
sunjin09 said:
Mod note: help removed

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:
  • #4
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).
 
  • #5
deleted
 
Last edited:
  • #6
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:

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

1. What is a two variable limit?

A two variable limit is a mathematical concept that involves finding the limit of a function that has two variables, typically x and y, as they approach a specific point or value. This type of limit is also known as a multivariable limit.

2. How do you solve a two variable limit?

To solve a two variable limit, you must first determine the approach direction, either from the left or the right. Then, you can use algebraic manipulation or substitution techniques to evaluate the limit. In some cases, you may need to use advanced techniques such as L'Hopital's rule.

3. What is the purpose of solving a two variable limit?

The purpose of solving a two variable limit is to better understand the behavior of a function as it approaches a certain point or value. This can help in making predictions and analyzing the function's properties.

4. What are some common examples of two variable limits?

Some common examples of two variable limits include finding the limit of a function as x and y approach 0, or as they approach infinity. Other examples may involve finding the limit of a function at a specific point, such as (2,3).

5. What are some tips for solving two variable limits?

Here are some tips for solving two variable limits:

  • Identify the approach direction.
  • Try to simplify the function algebraically.
  • If possible, use substitution to evaluate the limit.
  • Use L'Hopital's rule if necessary.
  • Draw a graph to visualize the behavior of the function.

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