Final answer:
To evaluate the limit, one must simplify the expression and consider if direct substitution is possible or if other methods like L'Hôpital's Rule or polar coordinates are needed to resolve any indeterminate form.
Step-by-step explanation:
When evaluating the limit of a function at a particular point, in this case, the limit as (x,y) approaches (0,0) of the expression x²y²(9-3/x²y²), it is important to first simplify the expression, if possible, to see if the limit can be directly computed. We look for any forms of indeterminate nature like 0/0 or ∞/∞. In this problem, when we plug in (0,0), the term 9-3/x²y² would become undefined, so we cannot simply substitute the values in.
To solve this, we need to analyze the behavior of the function as it approaches the given point. If the simplified expression does not lend itself to directly finding the limit, we might have to apply L'Hôpital's Rule, consider different paths to the point, or use polar coordinates for elimination of the indeterminate nature. In this case, a further simplification or a detailed approach to understand the limit is needed.