Use a Maclaurin series in Table 1 to obtain the Maclaurin series for the given function.

Table 1

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1 2x" = 1 + x + x? + x + ... R = 1 n=0 00 x" e* = E- n=0 n! 1 + 1! R = 0 2! + 3! x2n+1 E(-1)" - x7 sin x = R = 00 ... (2n + 1)! 3! 5! 7! n=0 x? x* 00 E(-1)*. = 1 + 6! R = 0 cos x = (2n)! 2! 4! n=0 .5 x' + 7 x2n+1 x tan 'x = E(-1)". 2n + 1 R = 1 %3D 3 n=0 x" In(1 + x) = E(-1)"-1, R = 1 - | | 2 n=1 Σ k x" =1 + kx + k(k – 1) x² + 2! k(k – 1)(k – 2) (1 + x)* = E x3 +... R = 1 3! n=0 3. +