- #1

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- Homework Statement
- Please see below

- Relevant Equations
- Indeterminate forms

Indeterminate forms are: ##\frac{0}{0}, \frac{\infty}{\infty} , \infty - \infty, 0 . \infty , 1^{\infty}, 0^{0}, \infty^{0}##

My answer:

4, 9, 15, 17, 20 are inderterminate forms

1. always has a fixed finite value, which is zero

2. ##0^{-\infty}=\frac{1}{0^{\infty}}=\frac{1}{0}=\infty## so it never has a fixed finite value

3. always has a fixed finite value, which is one

5. ##\infty . \infty=\infty## so it never has a fixed finite value

6. ##\infty^{-\infty}=\frac{1}{\infty^{\infty}}=\frac{1}{\infty}=0## so it always has a fixed finite value

7. ##\infty^{1}=\infty## so it always has a fixed finite value

8. ##\frac{\infty}{0}=\infty## so it never has a fixed finite value

10. ##\pi^{\infty}=\infty## so it never has a fixed finite value

11. ##1.\infty=\infty## so it never has a fixed finite value

12. ##1^{-\infty}=\frac{1}{1^{\infty}}## , not sure about this one since ##1^{\infty}## is indeterminate form. My guess for this one is: ##\frac{1}{1^{\infty}}=\frac{1}{1}=1## so always has a fixed finite value

13. ##\frac{1}{-\infty}=0## so it always has a fixed finite value

14. ##\infty^{\infty}=\infty## so it never has a fixed finite value

16. ##\infty^{-e}=\frac{1}{\infty^{e}}=\frac{1}{\infty}=0## so it always has a fixed finite value

18. ##\frac{0}{\infty}=0## so it always has a fixed finite value

19. ##\pi^{-\infty}=\frac{1}{\pi^{\infty}}=0## so it always has a fixed finite value

Are my answers correct?

Thanks