# Re: questions???

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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:

: 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

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.

I do not begin with "the cross product of two
vectors" and grunt when I have to start over.

(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.

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