Dick said:You'll need to figure out the limit of arctan(x) as x->infinity and (-infinity). Put the calculator away and remember the definition of arctan.
An asymptote is a line or curve that a graph approaches but never touches. It can be either vertical or horizontal.
Vertical asymptotes are vertical lines on a graph that the curve approaches but never touches. They occur when the denominator of a rational function is equal to zero.
To find the vertical asymptotes of a function, set the denominator of the function equal to zero and solve for the variable. The resulting values will be the x-coordinates of the vertical asymptotes.
Horizontal asymptotes are horizontal lines that the graph approaches but never touches. They occur when the degree of the numerator is less than the degree of the denominator in a rational function.
To find the horizontal asymptote of a function, compare the degrees of the numerator and denominator. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote will be at y = 0. If the degrees are equal, the horizontal asymptote will be at the ratio of the leading coefficients. If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.