Find the functions with the following Maclaurin series (refer to Table 2). f(x) et sin x COS

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

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f(x) et sin x COS X -12 -15 + In(1+x) tan ¹x (1+x)a IM IM IM IM IMBIMBIM8 IM8 n! n=0 = 1+x+ (-1)" x 2n+1 (2n + 1)! (-1)"¹x2n (2n)! Maclaurin series = 1 n (-1)n-1n = TABLE 2 2! 3! (-1)^2n+1 2n +1 =X- + Σx"=1+x+x² + x³ + x² +.... Σ (₁) x² = 1 + ax - + 4! 5! Σ(-1)"x"=1-x+ x² = x³ + x² -. 6! + X 7! - + + 7/7+... a(a-1)² + 2! a(a - 1)(a-2), 3! +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