While functioning on some probability question, I had to advice $lim_x o infty arctan(x)$. I knew the prize intuitively together $pi/2$, yet i cannot number out how to prove that by elementary way (without resorting come $epsilon-delta$ arguments). How does one prove it (preferably, there is no resorting to L"Hopital"s rule)?

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The $arctan$ role is the inverse function of $$ an:left(-fracpi2,fracpi2 ight) ightarrowBbb R$$and due to the fact that this function is monotonically boosting then$$lim_x ofracpi 2 an x=+inftyiff lim_x o+inftyarctan x=fracpi2$$

$$lim_x o +infty arctan x = fracπ2$$ and also $$lim_x o -infty arctan x = -fracπ2,$$then in total$$lim_x o infty arctan x = fracπ2 eer-selection.comrmsgn(x).$$



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