Question:

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.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

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!