(Untitled)

[planetswaves]

So the AP exam is approaching and one thing is really bothering me. Indeterminate forms. I mean I know L'Hospital and everything, but, let's say you have a limit that equals infinity times zero. Is "indeterminate" the only way to express this??

Comments

[bobbymcr]

Infinity times zero is an indeterminate form, but it can often be expressed as the usual "infinity / infinity" form suitable for L'Hopital's rule.

For example, this is "infinity times zero":

lim (x -> infinity) x * e^(-x)

However, you can rearrange the terms to get it into a form where you can determine the actual value of the limit:

lim (x -> infinity) x / e^x

Now we have "infinity over infinity" which is still indeterminate; however, it's easy to see that e^x grows far faster than x and thus the value is zero.

[planetswaves]

Thank you, that clarifies a lot, but what if you get e^x/e^z? L'Hospital seems to fail there, and that was the particular problem which provoked my question.

[rainbowboicmu]

e^x / e^z = e^(x-z).....

[bobbymcr]

I don't know what z is supposed to represent there. A constant? A second variable? (is this a multivariate limit?)