Introduction to Mathematical Analysis I - 3rd Edition
114 4.5 Taylor’s Theorem Prove that lim h→0 f (x0 +h)−Pn(h) hn =0. (Thus, we have f (x0 +h) =Pn(h)+g(h), where gis a function that satisfies limh→0 g(h) hn =0. This is called the Taylor expansion with Peano’s remainder.)