Find the functions with the following Maclaurin series (refer to Table 2).

f(x) et sin x COS X -12 -15 + In(1+x) tan x (1+x)a IM IM IM IM IMBIMBIM8 IM8 n! n=0 = 1+x+ (-1)" x 2n+1 (2n + 1)! (-1)"x2n (2n)! Maclaurin series = 1 n (-1)n-1n = TABLE 2 2! 3! (-1)^2n+1 2n +1 =X- + x"=1+x+x + x + x +.... () x = 1 + ax - + 4! 5! (-1)"x"=1-x+ x = x + x -. 6! + X 7! - + + 7/7+... a(a-1) + 2! a(a - 1)(a-2), 3! ++. Converges to f(x) for All x All x All x |x| < 1 |x| < 1 |x| < 1 and x = 1 |x|1 |x | < 1