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The limit of a multi-variable function at a given point refers to the value the function approaches as the input variables get arbitrarily close to that point. Using the example equation f(x,y) = x^2y, we determined the limit as both x and y approach 0, by substituting these values into the equation, to be 0.
The student's question is missing the equations but to explain the concept, let's take an example equation: f(x,y) = x^2y. Here, we're asked to find the limit of this function as the point (x, y) approaches (0,0). The concept of a limit in this context is from multi-variable calculus. It refers to the value that the function approaches as the input (x, y) gets arbitrarily close to some point—(0, 0) in this case.
To solve this, you would substitute the values of x and y into the equation. So, if we plug in x=0 and y=0 into the equation, we get:
f(0,0) = (0)^2*(0) = 0
Therefore, the limit of the function f(x,y) = x^2y as (x,y) --> (0,0) is 0.
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