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how to prove limit exists or not?

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1

0

$begingroup$

I am having hard time understanding what is the correct way to prove whether the limit exists or not for two variable functions of those two functions.

I don't know how to solve the first limit.
In the second limit I've tried to use $$x=rcos theta, y=rsin theta$$
but it didn't help me. I tried to use Squeeze theorem and got stuck.

$$lim_(x,y)to(0,0)fracsin(x^n+y^n)x^n-1+y^n-1$$

$$lim_(x,y)to(0,0)fracx^2cdot y^5x^3+y^9$$

calculus limits

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edited yesterday

Rotemi K

asked yesterday

Rotemi KRotemi K

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Rotemi K is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

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  $begingroup$
  Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
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  yesterday
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Hi, thanks for the comment. what should I add/edit in the post?
  $endgroup$
  – Rotemi K
  yesterday
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You could edit your post, adding to it what you have done thus far.
  $endgroup$
  – José Carlos Santos
  yesterday
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Ok, thank you- edited.
  $endgroup$
  – Rotemi K
  yesterday
  

  
  
  
  

add a comment | 

1

0

$begingroup$

I am having hard time understanding what is the correct way to prove whether the limit exists or not for two variable functions of those two functions.

I don't know how to solve the first limit.
In the second limit I've tried to use $$x=rcos theta, y=rsin theta$$
but it didn't help me. I tried to use Squeeze theorem and got stuck.

$$lim_(x,y)to(0,0)fracsin(x^n+y^n)x^n-1+y^n-1$$

$$lim_(x,y)to(0,0)fracx^2cdot y^5x^3+y^9$$

calculus limits

share|cite|improve this question

edited yesterday

Rotemi K

asked yesterday

Rotemi KRotemi K

112

New contributor

Rotemi K is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
  $endgroup$
  – José Carlos Santos
  yesterday
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Hi, thanks for the comment. what should I add/edit in the post?
  $endgroup$
  – Rotemi K
  yesterday
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You could edit your post, adding to it what you have done thus far.
  $endgroup$
  – José Carlos Santos
  yesterday
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Ok, thank you- edited.
  $endgroup$
  – Rotemi K
  yesterday
  

  
  
  
  

add a comment | 

$begingroup$

I am having hard time understanding what is the correct way to prove whether the limit exists or not for two variable functions of those two functions.

I don't know how to solve the first limit.
In the second limit I've tried to use $$x=rcos theta, y=rsin theta$$
but it didn't help me. I tried to use Squeeze theorem and got stuck.

$$lim_(x,y)to(0,0)fracsin(x^n+y^n)x^n-1+y^n-1$$

$$lim_(x,y)to(0,0)fracx^2cdot y^5x^3+y^9$$

calculus limits

share|cite|improve this question

edited yesterday

Rotemi K

asked yesterday

Rotemi KRotemi K

112

New contributor

Rotemi K is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|cite|improve this question

edited yesterday

Rotemi K

asked yesterday

Rotemi KRotemi K

112

New contributor

Rotemi K is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|cite|improve this question

edited yesterday

Rotemi K

asked yesterday

Rotemi KRotemi K

112

New contributor

Rotemi K is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked yesterday

Rotemi KRotemi K

112

New contributor

Rotemi K is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked yesterday

Rotemi KRotemi K

112