My Math Forum Indeterminate Form of [0^0]

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 May 2nd, 2016, 06:49 PM #1 Newbie   Joined: Mar 2016 From: georgia Posts: 2 Thanks: 0 Indeterminate Form of [0^0] Can anyone tell me if there is a function where the immediate indeterminate form is of [0^0] but after L'Hopital's rule, it reduces to a number. However, it can't reduce to the value of 1. Any other value will work. Thanks.
 May 2nd, 2016, 08:02 PM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,635 Thanks: 2620 Math Focus: Mainly analysis and algebra $$\lim_{x \to 0} x^{k \over \log x} = \mathrm e^k$$ Last edited by v8archie; May 2nd, 2016 at 08:20 PM.
 May 2nd, 2016, 08:09 PM #3 Member   Joined: Apr 2015 From: USA Posts: 46 Thanks: 32 v8archie, maybe you meant to write $\displaystyle\lim_{x\to0}x^{\frac{\log k}{\log x}}=k$
 May 2nd, 2016, 08:20 PM #4 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,635 Thanks: 2620 Math Focus: Mainly analysis and algebra Not quite, but thanks for pointing out the error.
 May 3rd, 2016, 12:06 AM #5 Senior Member   Joined: Jun 2015 From: England Posts: 905 Thanks: 271 If k is a constant then ln(k) and exp(k) are also constants so there is no point having a fancy expression of the constant.
 May 3rd, 2016, 01:37 AM #6 Newbie   Joined: May 2016 From: italy Posts: 22 Thanks: 0 the tricky part is this if you have some sort of f(x)^g(x) that goes to 0^0 or 1^0 or infinity^infinity in the most cases you can do e^g(x)lim f(X) and then do your derivite in some cases after this step you going to have another form of indeterminant like 0 over 0 or infinity over infinity and then you can apply hopital rule best wishes
May 3rd, 2016, 11:40 AM   #7
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Quote:
 Originally Posted by programmer the tricky part is this if you have some sort of f(x)^g(x) that goes to 0^0 or 1^0 $\displaystyle \ \ \ \ \$That isn't an indeterminate form. or infinity^infinity $\displaystyle \ \ \ \ \$That isn't an indeterminate form.
$\displaystyle On \ \ the \ \ other \ \ hand, \ \ 1^{\infty} \ \ and \ \ {\infty}^0 \ \$ are indeterminate forms.

 May 3rd, 2016, 01:45 PM #8 Newbie   Joined: May 2016 From: italy Posts: 22 Thanks: 0 yes exactly sorry about that and thanks to mentioned

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