(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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

**Physics Forums | Science Articles, Homework Help, Discussion**