Find the taylor polynomial

Question

Find the Taylor polynomial p₄ for f(x)=1/x³ at x=2.

Answer 1

Taylor approximation at point a=2 is given by:

P₄ = f(a) + ( f⁽¹⁾(a)(x-a)) / 1! + ( f⁽²⁾(a).(x-a)² )/2! + ( f⁽³⁾(a) (x-a)³ )/2! + ( f⁽⁴⁾(a) (x-a)⁴ )/4!

where f⁽ⁿ⁾(a) is the nth derivative of f(x) calculated at point a=2.