proof of L'Hopital rule #1371
proof of L'Hopital rule #1371
Conversation
theories/realfun.v
Outdated
|
|
||
| Section lhopital. | ||
| Context {R : realType}. | ||
| Variables (f df g dg : R -> R) (a : R) (U : set R) (Ua : nbhs a U). |
There was a problem hiding this comment.
As usual, a question about boundary conditions. I'm a bit surprised to see we require f to be derivable in a full neighborhood of a. But then only take the right/left limit. Instead I would expect to see either a^'- U or a^'+U depending on the direction of the limit. Will the theorem still go through with that weakening?
There was a problem hiding this comment.
Good catch - I think this should go through, but changes are a bit more time-consuming than I expected so still in progress, should be done sometime next week.
There was a problem hiding this comment.
@ndslusarz do you have progress to share?
There was a problem hiding this comment.
Sorry, forgot to send an update before xmas - unfortunately not a major update, haven't been able to make it work for the restricted neighbourhoods (but still think it should be possible, so I'll get back on that). I could push the unfinished version in the meantime if you'd like?
|
moved the lemmas to |
Motivation for this change
Co-authored by: @affeldt-aist @hoheinzollern
Proofs of L'Hopital rule for limits taken on left and right, and Cauchy's mean value theorem.
Checklist
CHANGELOG_UNRELEASED.mdReference: How to document
Reminder to reviewers