lim x^(x^(1/x))^(x^(1/x))^(x^(1/x))^(x^(1/x))^(x^(1/x))^(x^(1/x))^(x^(1/x))^(x^(1/x))^(x^(1/x))^(x^(1/x))^(x^(1/x))^(x^(1/x))-x-(log x)^2 as x-> inf

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