lim(2-x)tan(πx/2)

X->1

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- Oct 20th 2007, 01:54 PMwinterwyrmlets see if you can get this beast
lim(2-x)tan(πx/2)

X->1 - Oct 20th 2007, 02:01 PMCaptainBlack
- Oct 20th 2007, 02:01 PMTD!
Seems rather trivial. Perhaps you mean the following?

- Oct 20th 2007, 02:05 PMwinterwyrm
sorry, it's actually lim (2-x)^tan(Pi x/2)

as x approaches 1

I tried the formatting from word, and it didn't quite work - Oct 20th 2007, 02:07 PMtopsquark
- Oct 20th 2007, 02:11 PMTD!
That's correct. Does this help you?

- Oct 20th 2007, 02:16 PMtopsquark
- Oct 20th 2007, 02:21 PMwinterwyrm
isn't tan(Pi x/2) indeterminate though? I've tried tons of tricks, and I can't seem to crack any way to get the pi x/2 out of there.

- Oct 20th 2007, 02:24 PMTD!

Now you can apply l'Hôpital's rule. - Oct 20th 2007, 02:27 PMtopsquark
- Oct 20th 2007, 02:31 PMwinterwyrm
whoa, you guys are awesome, but do you have to handle different indet forms differently? if so, do you just tackle it by taking the derivative? I derivatived it before using the ln/exp rule, every time, lol. Thanks a million to everyone.

- Oct 20th 2007, 02:33 PMTD!
You can only apply l'Hôpital's rule (so f/g -> f'/g' for the limit) to the indeterminate forms 0/0 or ∞/∞. If you have another indeterminate form (0.∞, 1^∞, ...), you have to reduce it to one of the "allowed" indeterminate forms for l'Hôpital's rule.

- Oct 20th 2007, 02:37 PMCaptainBlack
- Oct 20th 2007, 02:38 PMtopsquark
- Oct 20th 2007, 02:39 PMTD!
Yes, although I prefer the way of rewriting as I did (log(...)/cot(...)) because log is easier to differentiate than 1/log.