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".
(0+)^(0+)
(0+)^(0-)
(0+)^(1-)
(0+)^inf
(0+)^(-inf)
(0-)(inf)
(0-) / (0-)
(0+) / (-inf)
(1-)(inf)
(1-)^(inf)
(1+)^(-inf)
(inf)^(1-)
(1-)^(0+)
(0-)^(1+)
(1-) / (0-)
(inf)^(-inf)
(-inf)^(inf)
(inf) - (-inf)
(inf)^(0-)
(1+) - (1-)
Give an indeterminate form that does not appear in any of the above problems.