(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the limit of f(x,y) = [itex]\frac{x^{2}-y^{2}}{\sqrt{x^{2}+y^{2}+81}-9}[/itex]

as (x,y) [itex]\rightarrow[/itex] (0,0)

3. The attempt at a solution

Ok, I looked at the examples in the book, and it seems pretty straight forward... I first look at f(x,0) to see what happens as we approach along the x-axis. The equation becomes 0/0, which is indeterminate. I did the same thing for f(0,y) to see what happens as we approach along the y-axis, which is also indeterminate. This would mean that the limit doesn't exist, according to the book. I even also approached on a different line, y=x, but that is also indeterminate.

That is the wrong answer however, according to the software. I thought maybe I would have to use l'hopital's rule for limits, but I'm not sure if I am supposed to do that, or if I would need to do it twice (with respect to x AND y). I started to take the partial with respect to x and it got very messy, so I wasn't sure if that was what I needed to do.

This is the very first question we are assigned on limits in calc 3.

EDIT:

I also just tried setting [itex]\sqrt{x^{2}+y^{2}+81}\neq9[/itex] and I got that y cannot be equal to plus or minus x, but I'm not really sure what to do with that.

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# CALC III Finding limits for a function of two variables.

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