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 Posted: Wed Mar 26, 2008 4:21 am
okay, so I have a function that a x approaches infinity it approaches 1, and then it is taken to the powr of infinity.
Will it still equal 1?
Does it depend?
I'm on a high, it's midnight and I'm working on assignment.
I'm trying to work out the lim as x -> inifinty of (x/(x+1))^x.
See the inside gos to 1 as x-> infinty, but what about the power to infinty?
1^infinty is 1, but it is not quite 1.
-sigh-
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Posted: Wed Mar 26, 2008 3:19 pm
You can't take the limit of the base and then raise that to the limit of the exponent; you have to consider the entire expression.
I'm pretty sure that the expression goes to 0 in the limit. The derivative is negative and the first few terms get small fairly quickly.
[EDIT] Sorry, brainfart. (x/x+1) = 1/(1+1/x), and since the limit of (1+1/x)^x as x goes to infinity is e, the limit of (x/x+1)^x as x goes to infinity is 1/e.
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