• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Multivariable limit

  • Thread starter Stevo6754
  • Start date
1. Homework Statement
Lim (x,y)->(1,1) of (x^2 + y^2 - 2) / (x^2 - y^2)


2. Homework Equations
None


3. The Attempt at a Solution
not continuous..

so I thought I would approach 1 from both x and y axises

lim x->1 (x^2 - 2)/(x^2) = -2
limt y->1 (y^2 - 2)/(-y^2) = 2

Does not exist right? Am I going about this the correct way?
 

HallsofIvy

Science Advisor
Homework Helper
41,681
864
No, you are not looking at it properly- you can't get to (1, 1) along the x or y axes! On the x-axis, y= 0 so, as x goes to 1, you are going to (1, 0), not (1, 1). Similarly, on the y-axis, x= 0 so, as y goes to 1, you are going to (0, 1), not (1, 1).

You could, instead, try approaching (1, 1) along the line y= 1 and then along the line x= 1. Now, with y= 1, the function becomes [itex](x^2+ 1- 2)/(x^2- 1)= (x^2- 1)/(x^2- 1)= 1[/itex] and, with x= 1, [itex](1+ y^2- 2)(1- y^2)= (y^2- 1)/(1- y^2)= -1[/itex].
 

Related Threads for: Multivariable limit

  • Posted
Replies
1
Views
890
  • Posted
Replies
3
Views
928
  • Posted
Replies
4
Views
1K
  • Posted
Replies
3
Views
853
  • Posted
Replies
3
Views
799

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top