Gerry Myerson <email@example.com> wrote: | | Robin Chapman <firstname.lastname@example.org> wrote: | > | > My objection to L'Hopital is mainly pedagogical. I've found that | > students immediately latch on to this rule, and will try to use | > it in *every* situation. It's depressing to see them fill three sides | > of A4 with a L'H rule that needs to be iterated a few lines when | > say, a series expansion will do it in two lines. | | I find it even more depressing to see them "use" L'H to evaluate | limit as x -> 0 of (cos x)/x.
An interesting L'Hospital pitfall is the following erroneous deduction
(1 - f) g 1 - f if g -> 1 then --------- -> ----- -> 1 1 - f g 1 - f
especially when f and g are (truncations of) certain power series.