one final exam down, one more to go (from the instructor's viewpoint).

currently i'm trying to finish writing my analysιs final exam. i'm beset by two "dangerous" tendencies in an instructor:

1. never mind, i can't ask them that;
   it's not in the syllabus.
2. this would be pretty cool, but .. hold on:
   
   if i think it's "cool,"
   then likely it's too hard for the students ..\-:

on a barely related note, earlier in the semester i showed this problem to the students,

Evaluate $\lim_{x \to \infty} \frac{x}{\sqrt{x^2+1}}$.

if only to convince them: sure, you can apply l'hοpital's rule, but that doesn't mean that it always works.

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in other news, i gave up on the preprint at around 2:15am or so. there will always be problems with exposition, but at least the proofs are fixed (maybe slightly polished).