Evaluating Multivariable Limit: (x^2+y^2)/(1+y^2)

[marquitos]

Multivariable Limits!

Lim (x^2+y^2)/(1+y^2)
(x,y)--> (0,0)

evaluate the limit or determine that it does not exist.
Im pretty sure that the limit does not exist because if i take it from the y and x axises the values don't match up but not really sure if that is the right way to do it. Any help would be great thank you very much.

 

[marquitos]

i apologize i think may be a very stupid question since simple substitution should most likely work but if it doesn't please inform me what i am doing wrong! Thank you again.

 

[Dick]

i apologize i think may be a very stupid question since simple substitution should most likely work but if it doesn't please inform me what i am doing wrong! Thank you again.

The denominator approaches 1, doesn't it? I'm pretty sure the limit does exist.

 

[deluks917]

Its a theorem that if f, g are continuous and g(x) != 0 then f/g is continuous at x. (1 + y^2) and (x^2 + y^2) are both continuous and (1+y^2) is never zero. Hence (x^2 + y^2)/(1+y^2) is continuous everywhere. So the limit is the value of the function at all points including zero.