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Question
Hi David,

I quite don't get limits of multivariable calculus and how the properties of limits apply to them. For example I don't quite how to do , lim (x,y)-->(-1,3) ((x^2-xy)/(2x+y)).

Thanks,
Sam

Answer
In general this is a hard question, for example you probably have encountered functions where you can approach the point along any line and get one answer but the limit doesn't exist because if you approach along a parabola you get a different answer.

The basic theorem from calc one holds though, by definition a function is continuous at a point if you can get the limit just by plugging in. Since x^2-xy and 2x+y are both polynomials, they are continuous. This means their quotient is also continuous, where defined.

Since the denominator is not zero at (-1,3) the function is defined there and continuous, so you can get the limit just by plugging in.

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David Hemmer

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