why is one to the power infinity considered indeterminate?

Answer 1

" indeterminate" means that from the behavior of the functions involved you can't say,without further calculation the existence or value of the limit
Let's take f^g if f=>a and g=>b f^g=>a^b
but if f=>1 and g=>infinity you don't know ,without more calculations,what is going on
(1+1/x)^x x=> infinity has limit e

1+2/x)^1/x x=> infinity has limit e^2
and in both cases the base =>1 and the exponent to infinity

Answer 2

IS it indeterminate? There is an answer to "one to the power infinity": the answer is "1".

After all, one to the power infinity is 1x1 and then that product times 1 (which is simply 1x1 again) an infinite number of times. That seems pretty determinate to me.

Answer 3

Because if we calculate the limit of 1^x as x approaches infinity we get 1.

OTOH, if x approaches infinity (1 + 1/x) approaches 1
But, the limit x-> infinity (x + 1/x)^x is e.

Answer 4

It is not indeterminate, but it is determinatable and the answer is 1.