Thread: Limits in two Dimensions

1. Limits in two Dimensions

How can I calculate the following limits or prove that don't exist:

a) $\lim_{(x,y) \to (0,0)} \frac {x^4 + y^4}{x^2 + y^2}$

b) $\lim_{(x,y) \to (0,0)} \frac {x^2 - y^2}{x^2 + y^2}$

Thanks in advance

2. Originally Posted by ypatia
How can I calculate the following limits or prove that don't exist:

a) $\lim_{(x,y) \to (0,0)} \frac {x^4 + y^4}{x^2 + y^2}$

b) $\lim_{(x,y) \to (0,0)} \frac {x^2 - y^2}{x^2 + y^2}$

Thanks in advance
Hi

a) $\frac {x^4 + y^4}{x^2 + y^2} \leq x^2+y^2$

b) On the x axis $\frac {x^2 - y^2}{x^2 + y^2} = 1$ but on the y axis $\frac {x^2 - y^2}{x^2 + y^2} = -1$