Final answer:
The question pertains to a function in multivariable calculus or real analysis that requires determining properties like continuity or differentiability, particularly around the origin by using limits.
Step-by-step explanation:
The student has asked about the function f: ℝ² → ℝ given by:
f(x, y) = (y³ - x¸y) / (x¶ + y²) if (x, y) ≠ (0, 0)
0 if (x, y) = (0, 0)
This is a question related to multivariable calculus or real analysis, where the student might be trying to understand the properties of this function, such as continuity or differentiability. To analyze the function's behavior, particularly around the origin, one might use limits. For example, to check for continuity at the origin, find the limit as (x, y) approaches (0, 0). If the limit exists and equals the function's value at the origin, which is given as 0, then the function is continuous at that point.