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:
IND: 0/0
0: 0/1
DNE: 1/0
Note that Hospital's rule (in some form) may ONLY be applied to indeterminate forms.
1. 1/-[infinity]
2. 0 - [infinity]
3. 0[infinity]
4. [infinity][infinity]
5. 0−[infinity]
6. [infinity]−[infinity]
7. [infinity]−e
8. 1[infinity]
9. π−[infinity]
10. π[infinity]
11. 1 −[infinity]
12. [infinity]1
13. [infinity]−[infinity]
14. 0/[infinity]
15. [infinity]0
16. 00
17. 10
18. 1 - [infinity]
19. [infinity]/0
20. inf - inf

Answer 1

Explanation:

1. 1/-[infinity] = 0

2. 0 - [infinity] = -∞

3. 0[infinity] = 0

4. [infinity][infinity] = IND

5. 0−[infinity] = -∞

6. [infinity]−[infinity] = ∞

7. [infinity]−e = ∞

8. 1[infinity] = ∞

9. π−[infinity] = -∞

10. π[infinity] = ∞

11. 1 −[infinity] = -∞

12. [infinity]1 = ∞

13. [infinity]−[infinity] = ∞

14. 0/[infinity] = IND

15. [infinity]0 = 0

16. 00 = 0

17. 10 = 10

18. 1 - [infinity] = -∞

19. [infinity]/0 = DNE

20. inf - inf = ∞