Arctangent is of Exponential Order Zero
Theorem
Let $\arctan: \R \to \openint {-\dfrac \pi 2} {\dfrac \pi 2}$ be the real arctangent.
Then $\arctan$ is of exponential order $0$.
Proof
Follows from Function with Limit at Infinity of Exponential Order Zero.
$\blacksquare$
In particular: limit of $\arctan$.
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