Find the Taylor series generated by f at x = a. f(x) =, 1 a = 6 (- 1)"(n+ 1)(x – 6)" Q A. 2

2. Fill in the table to find the first four terms of the Taylor Series for f(x) = cos(2x) if a = 8 n 0 1 2 3 f(n) (x) f(m) (a) C₁

1. Find the Fourier series of f(x) = x² F(-2)? - x defined for -2 ≤ x ≤ 2 if ƒ (x + 4). What is BONUS: Truncate the series to n = 3, 5, 10. Plot the 3 series in one graph. What is F(−2) for each?

For number 16, I am having trouble figuring out where the (k-1)!  came from. (Circled in pink in answer key)