Not so much a homework problem as a curiosity on my part. I chose to give a presentation recently on undefined numbers. With that, indeterminate's unsurprisingly found their way into my presentation.(adsbygoogle = window.adsbygoogle || []).push({});

After reading up on the list of indeterminate forms, I stumbled upon the form [tex]0^\infty[/tex] and for the life of my couldn't think of any examples in limits that have this form.

In my mind, I see such indeterminates as [tex]1^\infty[/tex] as trying to say

"multiplying 1 by itself repeatedly obviously still gives 1, but we're trying to do it so many times that it finally equals something other than 1".

Such an example would be e:

[tex]\lim_{x\rightarrow \infty}\left(1+\frac{1}{x}\right)^{x}[/tex]

Now a quick example of [tex]0^\infty[/tex] would be [tex]\lim_{x\rightarrow \infty}\left(\frac{1}{x}\right)^x[/tex]

but in a way, I see this as "enforcing" the answer zero since this limit tends to zero much faster than [tex]\lim_{x\rightarrow \infty}\frac{1}{x}[/tex] does.

So can anyone give me an example of such an indeterminate form that equals a finite, and possibly even infinite value.

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# Homework Help: List of indeterminate forms

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