Prove the statement of the following theorem for the sum function f + g : Let f, g E Cintl(x0 - h, xoth) for some h > 0 .If cER and the Taylor derivatives of the functions f and g are f (x) = Ty (x; xo) + Rin-1 (2; xo) and g(x) = In (x; no) + Rin+ (2; no) , then the Taylor derivative of the sum function f +g the development is (f + g) (2) = (In (2; 20) + Ti (20; 20)) + (Run+1 (20; 20) + Pin+1 (20; 20)) and the Taylor development of the function of is (cf) (2) = CTHi (x; x0) + cRent1 (2; 20)