Re: how to solve this limit?

In article <21nl72dbld57kiq6pc733rvigmc3465s7m@xxxxxxx>,
David C. Ullrich <ullrich@xxxxxxxxxxxxxxxx> wrote:

HInt: If f''(0) exists, then [f(x) - f(0) - f'(0)x]/x^2 ->
f''(0)/2 as x -> 0.

PS: Stop top-posting.

L'Hopital's rule does work, of course.

Golly. Accusing Wade of suggesting L'Hopital; this could be bloody.

That was my reaction too at first. Then I realized LHR gives a
quick and tidy proof of the result I stated: Apply it once and
then invoke the definition of f''(0). Usually when LHR is
deployed, it's much like the Pentagon: slower, dumber,
unnecessary, zero learning accomplished. Here I can't say that.

He didn't say anything about L'Hopital, btw. What he said is just
Taylor's theorem.

Not quite Taylor's theorem as far as I can see. I'm only assuming
f''(0) exists, not that f is C^2 near 0 (although the latter is
fine for the original problem).
.

Loading