find the fourth taylor polynomial of f(x)=1/x at x=2

Answer 1

f(x) = 1/x

f(2) = 1/2
f'(2) = -1/4
f''(2) = 2/8
f'''(2) = -6/16
. . .
f(x) = 1/0! f(2) + 1/1! f'(2) (x-2) + 1/2! f''(2) (x-2)^2 + ...

f(x) = ∑(-1)^k/2^(k+1) (x-2)^k