March 6, 2017
I've decided it would be fun to post a challenge problem every once in a while.
As a general rule, they'll be problems I come up with on my own, but I won't discount the possibility that they have already been posed.
At the same time, they should be problems that are accessible to students who have only just begun studying math as an undergrad. By accessible, I don't mean that anyone could figure it out. I mean that anyone could understand the solution if it was explained to them.
Anyways, here's the first one.
Let \(f(x) = \lim_{n\rightarrow\infty}|x|^{|x-1|^{|x-2|^{.^{.^{.^{|x-n|}}}}}}\)
What is the domain of \(f\) in \(\mathbb{R}\)? In \(\mathbb{C}\)?
Describe \(f\).