Good question. Picture the graph of arctan... can you? This is just the graph of tan reflected through the line y=x. It is almost like a tan function lying down. Since the x values of the restricted tan function go from -pi/2 to pi/2, with vertical asymptotes at those values of x. The inverse will have horizontal asymptotes at y=-pi/2 and y=pi/2. Particularly, as x-> infinity, arctan(x) -> pi/2 and as x-> -infinity, arctan(x) -> -pi/2. Hope that helps!
Good question. Picture the graph of arctan... can you? This is just the graph of tan reflected through the line y=x. It is almost like a tan function lying down. Since the x values of the restricted tan function go from -pi/2 to pi/2, with vertical asymptotes at those values of x. The inverse will have horizontal asymptotes at y=-pi/2 and y=pi/2. Particularly, as x-> infinity, arctan(x) -> pi/2 and as x-> -infinity, arctan(x) -> -pi/2. Hope that helps!
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