There was a question on a previous assignment I had trouble completing. I was unable to fully solve it before it was due, unfortunately, but I need to know how to do it. For this problem, we had to evaluate the following limit: lim x2y2   _______ (x,y) -> (0,0) x4+y4 If the table is difficult to read, this was the limit as (x,y) approaches (0,0) of the expression (x2*y2)/(x4*+y4). I thought I had to convert to polar coordinates but the result I got was dependent on theta, which should not have happened. What method should I have used, and what should the result of this limit have been?

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Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0). The multivariable limit of this function as it approaches the points (x0, y0) and is denoted as: