lim(x→+∞)〖x(π/2-arctan x)〗

(π/2-arctanx)/(1/x)
Type 0 / 0, using the lobita rule
Molecular derivation = - 1 / (1 + X & sup2;)
Denominator derivation = - 1 / X & sup2;
So = x & sup2; / (1 + X & sup2;) = 1 / (1 / X & sup2; + 1)
So limit = 1
So the original limit is 1

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