The Taylor Series Formula

Approximating Functions

A Taylor series allows us to represent complex functions (like sin(x) or e^x) as an infinite sum of polynomial terms. This is how calculators compute Sine and Cosine!

General Formula (centered at a):

f(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3! + ...

Maclaurin Series (centered at 0):

A special case where a = 0. Example for e^x:

e^x ≈ 1 + x + x^2/2! + x^3/3! + ...