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Out of curiosity, is anyone aware of a kind of generalization for l'Hopital's Rule from analysis for differentiable maps between differentiable manifolds? I'm having trouble formulating if I could do it or not, because (as far as I know), if I have ##f,g:M\to N##, with ##f## and ##g## differentiable and ##M## and ##N## differentiable, ##f(x)/g(x)## is not, in general, defined.

Again, I don't know if it can be generalized. Ideas are certainly welcome, since I'll probably be stuck thinking about it until I prove something does work or doesn't work.