- Showing a limit doesn’t exist by showing that it would have
different values along different paths
- How about an example where you don’t know whether the limit exists or not?
- Try both possibilities, starting with whatever seems most plausible, but being willing to switch between them as needed
- We weren’t able to see a solution to this during the session, but afterwards a second path occurred to me
- (Problem-solving moral here is that it can be really helpful
to set aside a problem you’re stuck on and come back to it
a little later)
- My tactic on such problems tends to be to get as much as I can from the gradients first, then finish with the constraints
- Periodically stepping back to look for strategy ideas in the big picture helps
- These are big and ugly — look for symmetries and similar simplifications
