I know that ,
$1) \frac{0}{0}$
$2) \frac{\pm\infty}{\pm\infty}$
$4) 0 \times(\pm\infty) $ are Indeterminate forms.
But in measure theory $ 0 \times(\pm\infty) =0 $
Are there any other indeterminate forms ? And Why ?
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asked Dec 19, 2015 at 1:02
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5$\begingroup$ You can add $1^{\infty}$ and $0^0$ to that list. $\endgroup$– JimmyK4542Dec 19, 2015 at 1:03
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1$\begingroup$ There's also $\infty - \infty$, $\infty^0$ $\endgroup$– Ben GrossmannDec 19, 2015 at 4:23
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3$\begingroup$ "Indeterminate form" really shouldn't be taken to have a hard, well-defined meaning. Division by zero and general arithmetic with infinity is not allowed by the rules of algebra. "Indeterminate forms" are just expressions which naively substitute a limiting value for the limit variable. $\endgroup$– Tac-TicsDec 19, 2015 at 6:34
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2 Answers
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The following is a list of indeterminate forms usually encountered:
$$\frac{0}{0}$$ $$\frac{\infty}{\infty}$$
$$0 \cdot \infty$$ $$0^0$$ $$\infty - \infty$$ $$\infty^0$$ $$1^\infty$$
Why are they indeterminate?
Just in case this turns out to be helpful:
The sources of these images are: 1. https://www.math.brown.edu/~pflueger/math1a/lecture24.pdf
In case, you are starting off learning about indeterminate forms I suggest taking a look at the pdf above. Hope this helps.
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$\begingroup$ L'Hospital can only be used in indeterminate formats \frac{0}{0} and \frac{\pm\infty}{\pm\infty} $\endgroup$ Sep 1 at 9:42
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Here are 7 indeterminate forms involving 0, 1, and ∞ that arise when evaluating limits
— Fermat's Library (@fermatslibrary) December 24, 2020
These are popularly known as the seven deadly sins of calculus.