Word Count : 457

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### Function: The given function is \( f(x, y) = \frac{2xy}{x^2 + y^2} \). ### Domain: The domain of the function refers to all the pairs \( (x, y) \) for which the function is defined. To find the domain, we need to ensure that the denominator \( x^2 + y^2 \neq 0 \). The denominator is zero when \( x = 0 \) and \( y = 0 \), which corresponds to the origin. Therefore, the function is undefined at \( (0, 0) \). Domain: \[ \boxed{ \{ (x, y) _____ ______ _____ ______ ____ ______ __________ ___.
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