Question

lim as t approaches infinity: arctan t

Answer 1

\[ \lim_{t \to \infty} \tan^{-1}(t) = 90^\circ = \frac{ \pi } {2} \]

Answer 2

Can you explain how it equals 90 degrees?

Answer 3

the arctangens function is defined as the restricted tan function, this is done because without that restriction the function wouldn't be injective.
You can find the graph here http://www.wolframalpha.com/input/?i=graph+tan%5E-1%28x%29

So the definition is that tan^{-1}(x) is the restricted tan(x) function with Domain \[D= \left[ -\frac{\pi}{2}; \frac{\pi}{2} \right]\]
So you see that the function stays even for large x within this domain.