Question

Guys help needed how to solve limits involving two variables such as this ;

lim (x,y->0,1) { ( x^2 +1) / ( x^2 + (y-1)^2 ) }

Thanks in advance .

Answer 1

...

Answer 2

Pick any path and parameterize it

Answer 3

Example :

Answer 4

$$\lim_{(x,y)\to(0,1)}\frac{x^2+1}{x^2+(y-1)^2}=\lim_{y\to1}\frac1{(y-1)^2}=\infty$$Let approach along the \(y\)-axis

Answer 5

Got that ; thanks the internet .

Answer 6

http://www.wolframalpha.com/input/?i=%28x%5E2%2B1%29%2F%28x%5E2%2B%28y-1%29%5E2%29

Answer 7

Better http://tutorial.math.lamar.edu/Classes/CalcIII/Limits.aspx

Answer 8

Yes... you pick any path and they should yield invariant limits

Answer 9

Thank you.