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

Limit of serverable variables, need help

  • Thread starter th3plan
  • Start date
  • #1
92
0

Homework Statement


(x,y)---> (0,0)
x²+y²/√(x²+y²+1) - 1

the -1 isnt in the square root, so people know




The Attempt at a Solution


i let y=o and got 2, and y=x² and x=y² and got 2, so how can i be sure this limit is 2, what other method must i try to be sure ?
 
Last edited:

Answers and Replies

  • #2
1,752
1
What exactly is the limit going to??? And your problem is very hard to interpret ... might want to re-type that with proper parenthesis.

let x=y
 
Last edited:
  • #3
HallsofIvy
Science Advisor
Homework Helper
41,792
920

Homework Statement


(x,y)---> (0,0)
x²+y²/√(x²+y²+1) - 1

the -1 isnt in the square root, so people know
But is it in the denominator? Is this [itex](x^2+ y^2)/(\sqrt{x^2+ y^2})+ 1[/itex] or [itex](x^2+ y^2)/(\sqrt{x^2+ y^2}+ 1)[/itex] ?



The Attempt at a Solution


i let y=o and got 2, and y=x² and x=y² and got 2, so how can i be sure this limit is 2, what other method must i try to be sure ?[/QUOTE]
One way to check is to change to polar coordinates. Since only r measures "distance to (0,0), if the limit, as r goes to 0, does not depend on [itex]\theta[/itex], that is the limit.
 

Related Threads for: Limit of serverable variables, need help

Replies
3
Views
4K
  • Last Post
Replies
1
Views
1K
Replies
2
Views
670
Replies
3
Views
958
Top