I have a general question with regards to multivariable analysis that is causing me quite some angst.... so we have a bunch of techniques to either establish that a limit exists or doesn't exist. And if need be we can be formal to find necessary $\delta$ and $\epsilon$.
What do we do when we are in higher dimensions? Even in two and three dimensions things get very messy vary quickly.......I can't imagine trying to bound a function of 25 degrees, even keeping track of the variables would be a nightmare.