Let f(x) be a function satisfying f(0) = 0, f'(0)=2, f"(0) = -2 and |f^(3) (x)| lessthanorequalto 6 for 0 lessthanorequalto x lessthanorequalto 1. Find the Taylor polynomial of degree 2 of f at x = 0 and then find lim_x rightarrow 0^+ 2x - f(x)/x^2. The Taylor polynomial of degree 2 of f at x = 0 is p_2(x) = Near x = 0, the function f(x) is equal to p_2(x) Plus some remainder, that is f(x) = p_2(x) + R_3(x). By the Lagrange formula for the remainder we know that R_3 (x) = f^(3) (c)/3! x^3 for some c [0, x]. Since |f^(3) (c)/3!| we deduce that lim_x rightarrow 0^+ 2x - f(x)/x^2 =