(Yes, I realize that this might be very obviously argumentative, but hopefully some response here will help understanding in how to deal with other 'meta' questions)
Hypothesis: Any question that is stated in the imperative, e.g. "Prove that..." "Show...", is homework whether tagged or not.
- if a question were not from another text, then any normal person would not word a question with the imperative ever.
- most people (here?) are normal
- so it is from another text, cut and paste or copied closely from another text.
- there are two (primary, not necessarily independent) reasons for copying from another text: one, since there is a question about it, possibly the wording, one needs to preserve the original to get the appropriate answer; two, because one is lazy.
- people who would ask a site like this for help on homework are probably lazy. Therefore, it is most likely that a person asking in the imperative is probably asking for help on homework.
- Given some of the explanation above, cut and paste is not so necessarily homework. People very reasonably can read a text not for a class, trying to do the exercises. And the best way to relate an exercise is verbatim (because the problem may be with the statement of the exercise).
- What's been typed and entered into a question box here is a pinhole camera onto the mind and intentions of the OP, it is impossible to second guess the intentions of the writer, and it's more robust to simply take things written at face value (that the imperative is simply unintended rudeness).
I don't have very good 'against' items because I am so convinced of 'for'.
I am fully aware that some people have been politely using the homework tags (but I'm sure most people omit tags not out of malice or but lack of knowledge, but then I'm sure they wouldn't bother with the tag if they knew).
So the question here then (to make a question out of it) is...do you find imperative mode to indicate homework? (and give your reasons either way)?