Evaluating limits Watch
- Thread Starter
- 08-04-2013 00:19
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- 08-04-2013 00:48
This may not be the neatest way to do it, but the way that occurred to me straight away was that it would be handy to work with logs because of the scary 1/x.
Hence the required limit is . (This works because exp and log are continuous functions, so limits pass between them.)
The argument of exp here is easy enough to evaluate with L'Hopital's rule (which was the obvious thing to use once we notice the "zero divided by zero" form).
- 08-04-2013 11:35
you can use the fact that, for any expression:
to turn the above (the entire thing in brackets) into an expression in "e" (looks more complicated, but leads to the answer)
you then get:
split the ln terms up to get: ln(a)-ln(b), then use the Maclaurin series expansion of the first term ( ), subtract the second (.
all terms drop out as x ->0 exept the term (e to the power of):
(EDITED)Last edited by Hasufel; 08-04-2013 at 12:21.
- 08-04-2013 12:34