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 .

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 .

anonymous · Answer

...

anonymous · Answer

Pick any path and parameterize it

anonymous · Answer

Example :

anonymous · Answer

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

anonymous · Answer

Got that ; thanks the internet .

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

Thank you.