Find the Maclaurin series for the function. Use the table of power series for elementary functions on page 674.

f(x) = cos 3x

POWER SERIES FOR ELEMENTARY FUNCTIONS Function X 1 (x-1) + (x 1)(x - 1) + (x - 1)4+ (-1)^(x - 1)" + 1 + x = 1- x + x-x + -1 + . .. In x = (x - 1) et = 1 + x sin x = x - cos x = 1 + arctan xx 1 3! 2! + arcsin x = x + (x-1)2(x-1) (x - 1)4 + + ps 5! + 2 T 7! 4! 6! + + + 5! 9! 8! x - + / - / + 3 5 7 3. 13 1.3x 2.3 2.4.5 + + + + (-1)" x +.. (-1)"xn+1 (2n + 1)! + +...+ (-1)" xn (2n)! 1.3.5x7 2.4.6.7 (-1)xm+1 2n + 1 + k(k-1)(k 2)x (1+x) = 1 + kx + k(k-1)x 2! 3! * The convergence at X = 1 depends on the value of k. +... +. + (-1)-(x-1)" n (2n)!xn+1 (2^n!)(2n + 1) +. + k(k-1). (k n! + .. n+1)x Interval of Convergence 0 < x < 2 -1 < x < 1 0 < x 2 -0 < x < -0 < x < -0 < x < 0 -1 x 1 -1 x 1 -1 < x < 1*