find the taylor series for f(x)=sin(x) centered at c=pi/2 on what interval is the expansion valid in interval notation

Find the Taylor series for f(x) = x³ + x² + x + 1 about a = = 1.

Find the 3rd derivative using finite difference approach via the Taylor series

I need help with these: a) Find the Fourier series of f(x) = |x| where −L < x < L. b) What is the Fourier series of the function f of period 2L defined byf(x) = -1 if −L < x< 0,f(x) = 1 if 0 < x < L,What does the series converge to when x = 0?