Why is 1^infinity indeterminate form and not just 1? Isn’t one to any power going to be 1?
In: Mathematics
1^infinity is just 1 as you say.
If you plot y = 1^x, you get a straight line which is the same as y = 1
Two possibilities for controversy.
* You can’t really plug ‘infinity’ into any equation. All you can say is that a function goes towards a limit as some value goes to infinity. lim x->infinity of 1^x is 1
* Are we really talking about exactly 1? Or is it something which goes towards 1? Say (1 + 1/x)… that goes towards 1 as x -> infinity but it’s not *exactly* 1. So if you have something like (1 + 1/x)^x and you look at how that behaves as x -> infinity. Then that won’t 1. That number will be *e* or ~2.718… But if it’s *exactly* one, then any power of it will also be 1.
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