I have been trying to do this problem for a couple of days but i cant seem to get the answer. Any help would be greatly appreciated.

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.

1. 0/infinity

2. (infinity)^(0)
3. (infinity)^(-e)
4. (infinity)/(0)

5.(infinity)^(-(infinity))
6. (infinity)-(infinity)

7. (0)^(-(infinity))
8. 1^(0)

9. (1)(infinity)

10. 0^(infinity)
11. pi^(infinity)

12. (0)(infinity)

13. 1^(-(infinity))

14. 0^(0)

15. 1^(infinity)

16. (infinity)(infinity)

17. (infinity)^(infinity)
18. (1)/(-(infinity))
19.pi^(-(infinity))

20. (infinity)^(1)

1. IND

2. IND
3. 0
4. DNE
5. 0
6. IND
7. DNE
8. 1
9. IND
10. 0
11. DNE
12. IND
13. 1
14. IND
15. 1
16. DNE
17. DNE
18. 0
19. 0
20. DNE

To determine the limit type for each form, we will analyze each case:

1. 0/infinity: This limit type is indeterminate (IND).

2. (infinity)^(0): This limit type has a fixed finite value. The numerical value depends on the specific context or problem.

3. (infinity)^(-e): This limit type never has a fixed finite value. It diverges to positive infinity, negative infinity, or oscillates (DNE).

4. (infinity)/(0): This limit type is indeterminate (IND).

5. (infinity)^(-(infinity)): This limit type never has a fixed finite value. It diverges to positive infinity, negative infinity, or oscillates (DNE).

6. (infinity)-(infinity): This limit type is indeterminate (IND).

7. (0)^(-(infinity)): This limit type never has a fixed finite value. It diverges to positive infinity, negative infinity, or oscillates (DNE).

8. 1^(0): This limit type has a fixed finite value. The result is 1.

9. (1)(infinity): This limit type is indeterminate (IND).

10. 0^(infinity): This limit type is indeterminate (IND).

11. pi^(infinity): This limit type never has a fixed finite value. It diverges to positive infinity, negative infinity, or oscillates (DNE).

12. (0)(infinity): This limit type is indeterminate (IND).

13. 1^(-(infinity)): This limit type never has a fixed finite value. It diverges to positive infinity, negative infinity, or oscillates (DNE).

14. 0^(0): This limit type has a fixed finite value. The result is 1.

15. 1^(infinity): This limit type has a fixed finite value. The result is 1.

16. (infinity)(infinity): This limit type is indeterminate (IND).

17. (infinity)^(infinity): This limit type never has a fixed finite value. It diverges to positive infinity, negative infinity, or oscillates (DNE).

18. (1)/(-(infinity)): This limit type has a fixed finite value. The result is 0.

19. pi^(-(infinity)): This limit type never has a fixed finite value. It diverges to positive infinity, negative infinity, or oscillates (DNE).

20. (infinity)^(1): This limit type never has a fixed finite value. It diverges to positive infinity, negative infinity, or oscillates (DNE).

I hope this helps! Let me know if you have any further questions.

To determine whether each of the given limit types is indeterminate, always has a fixed finite value, or never has a fixed finite value, you need to understand the concepts behind each limit type.

1. 0/infinity:
This limit is indeterminate because you have a zero in the numerator and infinity in the denominator. To evaluate this limit, you can use techniques like L'Hôpital's rule or algebraic manipulation.

2. (infinity)^(0):
This limit type never has a fixed finite value. When you have a base that approaches infinity and an exponent that approaches zero, the result can vary significantly depending on the specific values involved.

3. (infinity)^(-e):
This limit type never has a fixed finite value. When you have a base that approaches infinity and an exponent that is negative and finite, the result can vary significantly.

4. (infinity)/(0):
This limit type is indeterminate. When you have infinity in the numerator and zero in the denominator, the result can depend on the specific values and functional form involved.

5. (infinity)^(-(infinity)):
This limit type is indeterminate. When both the base and the exponent approach infinity, the result can depend on the specific values and functional form involved.

6. (infinity)-(infinity):
This limit type can have a fixed finite value or be indeterminate. It depends on the specific values involved and the functional form of the expression.

7. (0)^(-(infinity)):
This limit type never has a fixed finite value. When you have zero as the base and a negative infinity as the exponent, the result can vary significantly.

8. 1^(0):
This limit type always has a fixed finite value, which is 1. Any number raised to the power of zero equals 1.

9. (1)(infinity):
This limit type is indeterminate. When you have a finite number multiplied by infinity, the result can depend on the specific values involved.

10. 0^(infinity):
This limit type never has a fixed finite value. When you have zero as the base and infinity as the exponent, the result can vary significantly.

11. pi^(infinity):
This limit type never has a fixed finite value. When you have a constant (pi in this case) as the base and infinity as the exponent, the result can vary significantly.

12. (0)(infinity):
This limit type is indeterminate. When you have zero multiplied by infinity, the result can depend on the specific values and functional form involved.

13. 1^(-(infinity)):
This limit type never has a fixed finite value. When you have 1 as the base and a negative infinity as the exponent, the result can vary significantly.

14. 0^(0):
This limit type is indeterminate. Zero raised to the power of zero can result in different values depending on the specific context and the functional form involved.

15. 1^(infinity):
This limit type is indeterminate. When you have 1 as the base and infinity as the exponent, the result can depend on the specific values and functional form involved.

16. (infinity)(infinity):
This limit type is indeterminate. When you have infinity multiplied by infinity, the result can depend on the specific values and functional form involved.

17. (infinity)^(infinity):
This limit type never has a fixed finite value. When both the base and the exponent approach infinity, the result can vary significantly.

18. (1)/(-(infinity)):
This limit type never has a fixed finite value. When you have a finite number (1 in this case) in the numerator and negative infinity in the denominator, the result can vary significantly.

19. pi^(-(infinity)):
This limit type never has a fixed finite value. When you have a constant (pi in this case) as the base and a negative infinity as the exponent, the result can vary significantly.

20. (infinity)^(1):
This limit type is indeterminate. When you have infinity as the base and 1 as the exponent, the result can depend on the specific values and functional form involved.

It is important to note that the evaluation of these limit types requires a more detailed analysis that considers the specific context and functional form of the expressions involved. These general classifications provide an overview of the possibilities.