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Math Help - What are the indeterminate forms such that L'Hopital's rule can be used?

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    What are the indeterminate forms such that L'Hopital's rule can be used?

    \frac{0}{0}, \frac{\infty}{\infty}, 0\times{\infty},{\infty}^{\infty}, {\infty}^0,0^0, 1^{\infty}, \infty - \infty.

    How about 0^{\infty}? anything else?
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    Quote Originally Posted by crossbone View Post
    \frac{0}{0}, \frac{\infty}{\infty}, 0\times{\infty},{\infty}^{\infty}, {\infty}^0,0^0, 1^{\infty}, \infty - \infty.

    How about 0^{\infty}? anything else?
    Check wikipedia or a textbook.
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    You can go directly to L'Hospital's Rule if it's of the form \displaystyle \frac{0}{0} or \displaystyle \frac{\infty}{\infty}.

    However, you can apply some transformations to the other forms to get them to \displaystyle \frac{0}{0} or \displaystyle \frac{\infty}{\infty}.
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    Quote Originally Posted by crossbone View Post
    \frac{0}{0}, \frac{\infty}{\infty}, 0\times{\infty},{\infty}^{\infty}, {\infty}^0,0^0, 1^{\infty}, \infty - \infty.

    How about 0^{\infty}? anything else?
    The form 0^{+ \infty} is not 'indeterminate'!... more precisely if You have a function like y(x)= f(x)^{g(x)} with \lim_{x \rightarrow x_{0}} f(x)=0 and \lim_{x \rightarrow x_{0}} g(x)= +\infty is \lim_{x \rightarrow x_{0}} f(x)^{g(x)}=0...

    Are You sure that \infty^{\infty} is 'indeterminate'?...

    Kind regards

    \chi \sigma
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    MHF Contributor chisigma's Avatar
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    Other 'indeterminate forms' that are not reported in the 'holy books' and can be solved with l'Hopital's rule are [in my opinion...] \log_{0} 0 and \log_{\infty} \infty...

    Kind regards

    \chi \sigma
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    Quote Originally Posted by dwsmith View Post
    Check wikipedia or a textbook.
    I did but it didn't include 0^{\infty} even though  {\infty}^0 and 0^0 were. isn't it an indeterminate form?
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    First paragraph from this source ...

    http://spectrum.troy.edu/~andrew/doc...ETERMINATE.pdf

    ... lists "seven known" indeterminate forms.
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  8. #8
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    seems like it's not then. so what's the value of 0^{\infty} ? 0?
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    Quote Originally Posted by crossbone View Post
    seems like it's not then. so what's the value of 0^{\infty} ? 0?
    consider ...

    \displaystyle \lim_{n \to \infty} r^n when |r| < 1
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  10. #10
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    makes sense. thanks!
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