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Posted by T.Gracken on October 29, 2002 at 10:52:00:

: : : here's the question:

: : : find lim (tan2x)/(e^(3x)-1)
: : : x-->0

: : : I am lost! this is how i started:

: : : (lim sin2x/lim cos2x)/(lim e^(3x)-1) then I am stuck

: I don't see how you can solve this without using L'Hospital's Rule, so you probably should look that up. It's a very simple problem using that technique. But I'm intrigued enough to try again, so give me a clue. Where did you find this problem? Book/chapter, etc. Or if it was just assigned in class, what course & generally what topic are you up to?

I have not been able to determine the limit without L'Hospital's rule either. As Joel stated, with L'Hospitals rule it is extremely straigforward (and quick). Unless you know some interesting equivalent expressions or theorems, I don't see how it is to be done. (i tried factoring the denominator as a difference of cubes and rewriting the numerator with various identities. I also tried power series representations but stopped as those are generally discussed after L'Hospitals rule)

If this is an introduction problem to limits, I could only assume you are to set up a table of values. that is, a column of x-values that get closer to zero, and the evaluated expression at those values. then "see" if you can guess what value the expressions appear to converge to.

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