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More practice with indeterminate forms


Determinate whether or not each of the following is an "indeterminate form". If you believe it is an indeterminate form, try to give two examples of that form such that they have different limits (but this can be difficult, so don't worry if you can't think of such examples). If you believe it is not an indeterminate form, give the limit, if there is one -- this part you should do.

Note the following abbreviations:

For example, (0+)^(inf) means you're finding the limit of [f(x)]^[g(x)]  as x --> a , where f(x) approaches 0 from the right and g(x) goes to infinity as x --> a.
If you think about it, the form (0+)^(inf) is not indeterminate; the limit is always zero. So for your answer you could write "always --> 0".

  1. (0+)^(0+)

  2. (0+)^(0-)

  3. (0+)^(1-)

  4. (0+)^inf

  5. (0+)^(-inf)

  6. (0-)(inf)

  7. (0-) / (0-)

  8. (0+) / (-inf)

  9. (1-)(inf)

  10. (1-)^(inf)

  11. (1+)^(-inf)

  12. (inf)^(1-)

  13. (1-)^(0+)

  14. (0-)^(1+)

  15. (1-) / (0-)

  16. (inf)^(-inf)

  17. (-inf)^(inf)

  18. (inf) - (-inf)

  19. (inf)^(0-)

  20. (1+) - (1-)

  21. Give an indeterminate form that does not appear in any of the above problems.


Updated: 31 August, 2009 17:44:19