f(x)=lnx. the third degree polynomial for f about x=1 is?

Answer 1

f(x)= ln(x) f(1) = 0

f'(x) = 1/x f'(1) = 1

f"(x) = -1/x² f"(1) = -1

f"'(x) = 2/x³ f"'(1) = 2

f(x) ≈ f(1) + f'(1)(x-1) + f"(1)(x-1)²/2 + f"'(1)(x-1)³/6

≈0 + (x-1) - (x-1)²/2 +2(x-1)³/6

≈ x³/3 - 3x²/2 + 3x - 11/6