Topology

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Moderate

Continuous Function in R^2

TOPO-VEBVNC

Which of the following functions can be extended continuously to $\mathbb{R}^{2}$?

A

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

B

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

C

$\frac{xy}{x^{2}+y^{2}}$

D

$\frac{x^{3}}{x^{2}+y^{2}}$