Word Count : 289

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We are given the function: $$ f(x, y) = \frac{xy}{x^2 + y^2}. $$ First, consider the iterated limits. 1. Limit as $x \to 0$ then $y \to 0$: $$ \lim_{y \to 0} \lim_{x \to 0} \frac{xy}{x^2 + y^2}. $$ Step 1: Fix $y$ and take $\lim_{x \to 0}$: $$ \lim_{x \to 0} \frac{xy}{x^2 + y^2} = \frac{0 _____ ___ __________ ____ _____.
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