1. The problem statement, all variables and given/known data e^((ln(x))^2)=O(1)? as x->0 2. Relevant 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 3. 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.