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pivoxa15
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Homework Statement
e^((ln(x))^2)=O(1)?
as x->0
Homework Equations
g(x)=O(f(x)) => |g(x)|<K|f(x)| as x->0 in this case but can approach any value as desired.
K<infinity
The Attempt at a Solution
We can try numbers for small x but non zero that satisfy the inequality however are we allowed to manipulate infinities? Somehow I think that the equality shouldn't stand.
I know that x^2 does not equal O(x) when x->infinity but does equal when x->0
We can look at it this way, g(x)=O(f(x)) => |g(x)|<K|f(x)| as x->0, K<infinity => lim x->0 |g(x)/f(x)| is finite.
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