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Ignea_unda
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[SOLVED] Factorial Limits
lim n^n
x->00 n!
Instructor said to use the Squeeze theorem.
So far I have not been able to come up with much. I have looked at breaking the top apart into (n)(n)(n)...(n) and the bottom into n(n-1)(n-2)...(2)(1). My instinct when plugging numbers in for examples says that it should diverge, but when I apply Induction to prove this hypothesis, I get a contradiction. I know I'm over thinking this one (or at least I hope I am). Thanks for your help
Homework Statement
lim n^n
x->00 n!
Homework Equations
Instructor said to use the Squeeze theorem.
The Attempt at a Solution
So far I have not been able to come up with much. I have looked at breaking the top apart into (n)(n)(n)...(n) and the bottom into n(n-1)(n-2)...(2)(1). My instinct when plugging numbers in for examples says that it should diverge, but when I apply Induction to prove this hypothesis, I get a contradiction. I know I'm over thinking this one (or at least I hope I am). Thanks for your help