Taylor-Entwicklung: f(x) = COS(x), x0 = 0

f(x) = COS(x)

f'(x) = - SIN(x)

f''(x) = - COS(x)

f'''(x) = SIN(x)

Taylor-Polynom

T(x) = f(x0)/0!·x^0 + f'(x0)/1!·x^1 + f''(x0)/2!·x^2 + f'''(x0)/3!·x^3

T(x) = (COS(0))/1·x^0 + (- SIN(0))/1·x^1 + (- COS(0))/2·x^2 + (SIN(0))/6·x^3

T(x) = (1)/1·1 + (0)/1·x^1 + (- 1)/2·x^2 + (0)/6·x^3

T(x) = 1 - 1/2·x^2

Skizze