The horizontal asymptotes of the function f(x) = (cot^-1)(x^2 - x^4) are determined by analyzing the behavior of the function as x approaches positive and negative infinity. As x increases without bound, the expression x^2 - x^4 approaches negative infinity, leading to f(x) approaching π. Conversely, as x decreases without bound, the same expression also approaches negative infinity, resulting in f(x) again approaching π. Therefore, the horizontal asymptote for this function is y = π.
PREREQUISITESStudents studying calculus, particularly those focusing on asymptotic analysis and inverse trigonometric functions. This discussion is beneficial for anyone seeking to deepen their understanding of horizontal asymptotes in mathematical functions.
