List of Indeterminate forms in Mathematics

Question

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 ?

Answer 1

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

2. http://17calculus.com/limits/indeterminate-forms/

In case, you are starting off learning about indeterminate forms I suggest taking a look at the pdf above. Hope this helps.

Answer 2

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.