$\displaystyle \frac{0}{0}, \frac{\infty}{\infty}, 0\times{\infty},{\infty}^{\infty}, {\infty}^0,0^0, 1^{\infty}, \infty - \infty.$
How about $\displaystyle 0^{\infty}$? anything else?
$\displaystyle \frac{0}{0}, \frac{\infty}{\infty}, 0\times{\infty},{\infty}^{\infty}, {\infty}^0,0^0, 1^{\infty}, \infty - \infty.$
How about $\displaystyle 0^{\infty}$? anything else?
You can go directly to L'Hospital's Rule if it's of the form $\displaystyle \displaystyle \frac{0}{0}$ or $\displaystyle \displaystyle \frac{\infty}{\infty}$.
However, you can apply some transformations to the other forms to get them to $\displaystyle \displaystyle \frac{0}{0}$ or $\displaystyle \displaystyle \frac{\infty}{\infty}$.
The form $\displaystyle 0^{+ \infty}$ is not 'indeterminate'!... more precisely if You have a function like $\displaystyle y(x)= f(x)^{g(x)}$ with $\displaystyle \lim_{x \rightarrow x_{0}} f(x)=0$ and $\displaystyle \lim_{x \rightarrow x_{0}} g(x)= +\infty$ is $\displaystyle \lim_{x \rightarrow x_{0}} f(x)^{g(x)}=0$...
Are You sure that $\displaystyle \infty^{\infty}$ is 'indeterminate'?...
Kind regards
$\displaystyle \chi$ $\displaystyle \sigma$
Other 'indeterminate forms' that are not reported in the 'holy books' and can be solved with l'Hopital's rule are [in my opinion...] $\displaystyle \log_{0} 0$ and $\displaystyle \log_{\infty} \infty$...
Kind regards
$\displaystyle \chi$ $\displaystyle \sigma$
First paragraph from this source ...
http://spectrum.troy.edu/~andrew/doc...ETERMINATE.pdf
... lists "seven known" indeterminate forms.