x -> 0

What is the indeterminate form of

lim n-> infinity (1 + 7/n + x/n)^n

If I let u = (7+x)/n, the problem becomes

lim n-> infinity (1+u)^((7+x)/u)

And the answer is e^7, but I don't understand the process of obtaining the answer.

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- Sep 28th 2009, 12:57 PMsomaIndeterminate Form
x -> 0

What is the indeterminate form of

lim n-> infinity (1 + 7/n + x/n)^n

If I let u = (7+x)/n, the problem becomes

lim n-> infinity (1+u)^((7+x)/u)

And the answer is e^7, but I don't understand the process of obtaining the answer. - Sep 28th 2009, 11:10 PMmr fantastic
- Sep 29th 2009, 04:59 AMsoma
for:

How can I show the work on my homework assignment for that particular step? I know you say it's a standard limit, but I can't find any information about it online... Or is it just a matter of saying it's a standard limit?

- Sep 29th 2009, 05:18 AMJester
Here's a site

http://en.wikipedia.org/wiki/E_(mathematical_constant)

As for your problem, from

set noting that gives so

so

. - Sep 29th 2009, 05:31 AMsoma
That's perfect. I now understand the problem completely, thanks!