You are watching: Limit of inverse tangent as x approaches infinity
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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Proof that the limit of the normal distribution for a standard deviation approximating 0 is the dirac delta function.
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