Word Count : 416

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To determine whether the limit of \( f(x, y) \) as \( (x, y) \to (0, 0) \) exists, let's analyze the behavior of the function along different paths approaching the origin. The function is given by: \[ f(x, y) = \begin{cases} \frac{x^2 y}{x^4 + y^2} & \text{if } x^4 + y^2 \neq 0 \\ 0 & \text{if } x = y = 0 \end{cases} \] ### Step 1: Check the limit along the x-axis (i.e., \( y = 0 \)). When \( _______ ________ ________ ______ ___ __________ _____ _________ ____ _____.
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