Question

Find the taylor polynomial of degree 3 for f(x)=1/x+2


F(x)=-1/x+2)

Answer 1

well,
f = 1/(x+2)
f' = -1(x+2)^2
f" = 2/(x+2)^3
f⁽³⁾ = -6/(x+3)^4

So, the Taylor series at x=0 is

1/2 - x/4 + x^2/8 - x^3/16 + ...