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Answer :
According to the question we have the solution that The limit of the function does not exist at (2,4).
The given question involves finding the limit of a function at a specific point. Let's break it down step by step.
If this is the case, you can try to evaluate the limit by directly plugging in the values (2, 4) for (x, y) and see if the expression becomes indeterminate (such as 0/0 or ∞/∞), in which case you might need to use L'Hôpital's rule or another method to find the limit.
lim (x,y)→(2,4) (x² + x²y - 2y) / (x - vy):
It appears that you're trying to evaluate the limit of the expression as (x, y) approaches (2, 4). The limit you're trying to find involves v, but the exact expression you're using for v is unclear. It seems like you want to substitute v with y, but the notation is not very clear. If v is indeed intended to be substituted with y, the limit expression becomes:
lim (x,y)→(2,4) (x² + x²y - 2y) / (x - y) .
In this case, the two limits are not equal. Therefore, the limit does not exist at (2,4).
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