Posted by Soroban on August 31, 2002 at 01:55:21:
In Reply to: Re: questions??? posted by T.Gracken on August 29, 2002 at 20:32:56:
: How about this...
: use algebra to simplify [1 - e-x]/[ex - 1]
: that is;
: [1 - e-x]/[ex - 1]
: = [ex - 1]/[ex(ex - 1)] .......multiply numerator and denominator by ex
: = 1/(ex)
: so, from algebra, we can reduce the expression to a point where substitution is possible and the limit is 1.
: {that's right, same result!!!}
: does that work for you???
YES!
Well done, TG!
I was away for two days and saw this thread
just now. Had to read through all of it.
All that talk about L'Hopital was wearing me out.
I use it as a last resort - not the first.
Textbooks and professors usually expect some sort
of algebraic/trignometric manipulation to arrive
at an answer. If I'm not sure if the person
posting the question is at that level, I try to
find another (more elegant) approach. Usually,
I can tell from the level of the problem
whether L'Hopital is appropriate.
A problem like: lim (x^2 - 4)/(x - 2) as x -> 2
is probably at the beginning of Limits (pre-pre-
derivatives). It should be obvious that he/she
hasn't differentiated anything yet and, therefore,
has not heard of L'Hopital.
If someone asks about the area of a triangle,
I do not begin with "the cross product of two
vectors" and grunt when I have to start over.
Recently, someone asked about the limit of
(sin x)/x as x -> 0, using the "Squeeze Theorem".
Some clown, with his usual devastating brand of
acid sarcasm, said, "Ever heard of L'Hopital?"
I beginning to rant... sorry. I'll shut up now.