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• (가)$\displaystyle \lim _ {\left (x, y \right) \rightarrow \left (0, 0 \right)} {\frac{x^3} {x^2 +y^2}} =0$
• (나)$\displaystyle \lim _ {\left (x, y \right) \rightarrow \left (0, 0 \right)} {\frac{\sin \left (x^2 +y^2 \right)} {x^2 +y^2}} =1$
• (다)$\displaystyle \lim _ {\left (x, y \right) \rightarrow \left (0, 0 \right)} {\frac{x^2 -y^2} {x^2 +y^2}} =1$
• (라)$\displaystyle \lim _ {\left (x, y \right) \rightarrow \left (0, 0 \right)} {\frac{\sqrt {2x^4 +3y^5}} {x^2 +y^2}} = \sqrt 2$