Question

What are all the kinds of indeterminate forms you can have with infinity and 0?

Answer 1

i dont remeber all, 0/0;inf/inf;1^inf;inf-inf;0^inf

Answer 2

Well, there are an infinite number of indeterminate forms...those are definitely some of the most common noes though. However, I don't believe \(1^\infty\) is indeterminate.

Answer 3

@yakeyglee it's indeterminate for sure!

Answer 4

http://www.wolframalpha.com/input/?i=1%5Einf

Answer 5

Yeah, you're right. Whoops! For instance, on one hand, we have \[\lim_{x \rightarrow \infty} \left( 1+ \frac{1}{n}\right)^n=e,\]and on the other, \[\lim_{x \rightarrow \infty} \left( 1+ \frac{1}{n^2}\right)^n=1.\]