Finding limits of 2 varible functions

[tnutty]

Homework Statement

Find the limit, if exist, otherwise show why it doesn't;

F(x,y) = R;

where R =

x^2 + y^2
------------------------
sqrt( x^2 + y^2 + 1) - 1


Attempt :

|R| = R

Since I know that |x| <= sqrt(x^2) <= sqrt(x^2 + y^2 + 1) = J

R <= J^2 + J^2 / (J + 1) = 2*J^2 / (J + 1)

Stuck here.

Also does the methods of 1 variable function to find limits, such as l'hopital rule apply to 2 variable? I assume not, since the book has not mentioned it.

 

[lanedance]

i assume it is at the limit at the point (0,0) you're trying to investigate?

 

[Billy Bob]

Suggestion: Go back to the beginning and rationalize the denominator.

 

[tnutty]

Suggestion: Go back to the beginning and rationalize the denominator.

Perfect. Should have seen that. Thank you.