Find the Maclaurin series for the function. Use the table of power series for elementary functions shown below.

g(x) = arctan 5x

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POWER SERIES FOR ELEMENTARY FUNCTIONS Function X 1 (x-1) + (x - 1)²(x - 1)³ + (x - 1)4+ (-1)^(x − 1)² + ··· - 1 + x = 1x + ²x³ + x²-1³ +.. - - In x = (x - 1) et = 1 + x + sin x = x - cos x = 1 3! 2! arctan x = x = arcsin x = x + + +(-1) (x - 1)² (x-1)³ (x - 1)4 + 2 3 + 15 x7 5! 7! x4 4! 2.3 + 3 5 (1+x)= 1+ kx + The convergence at X = I 6! 15 x7 7 + + 5! 9! 18 8! 1.3x³ 2.4.5 k(k − 1)x² 2! + + + n! ±1 depends on the value of k. + (-1)"x²+1 (2n + 1)! + +. (-1)" x²n (2n)! 1.3.5x7 2.4.6.7 + k(k − 1)(k − 2)x³ 3! +. (-1)"x²n+1 2n + 1 · + +... (-1)"-¹(x-1)" n +... (2n)!x²n+1 (2"n!)²(2n + 1) ++ + . k(k-1) (kn+1)x + n! Interval of Convergence 0 < x < 2 -1 < x < 1 0 < x≤ 2 -∞0 < x < ∞0 -∞0 < x < ∞0 -∞0 < x < 00 -1 ≤ x ≤ 1 -1 ≤ x ≤ 1 -1 < x < 1*