For each of the following forms determine whether the following limit type is indeterminate, always has a fixed finite value, or never has a fixed finite value. In the first case answer IND, in the second case enter the numerical value, and in the third case answer DNE. For example:
For you would answer IND,
for you would answer 0,
and for you would answer DNE.
NOTE: If the answer is or , answer DNE, since infinite limits cannot strictly be said to exist.
Note that l'Hopital's rule (in some form) may ONLY be applied to indeterminate forms.
I apparently got 17 out of 20 of these right so which of these two did I get wrong and why? Also, I copied 1^infinity as being indeterminate from my book (got it right above) but would otherwise have guessed that 1^infinity = inifinity = DNE (in the context of this question) so could someone explain to me why it is wrong? My logic is that for example 1.00000000000001^huge number = inifnity. Another example try doing 1.01^2 and then 1.01^3 and so on and you will see that it keeps growing.
Any help would be greatly appreciated!
Thanks in advance!