Limits in two Dimensions

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March 24th 2009, 01:11 PM
ypatia

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
March 24th 2009, 01:22 PM
running-gag

Quote:

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 $\frac {x^2 - y^2}{x^2 + y^2} = -1$

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