Arccotangent is of Exponential Order Zero
Theorem
Let $\arccot: \R \to \openint 0 \pi$ be the real arccotangent.
Then $\arccot$ is of exponential order $0$.
Proof
Follows from Function with Limit at Infinity of Exponential Order Zero.
$\blacksquare$
In particular: limit of $\arccot$.
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