Suppose that h > 0 and f' exists and is finite for every x in (a-h,a+h). Also suppose that f is continuous on [a-h,a+h]. If f"(a) exists, show that the limit f(a+h) - 2f(a) + f(a-h) lim ------------------------- = f"(a) h→0 h^2 Note: 请顺便给一个反例 f(x), 使得左边的极限式存在, 但 f" 不存在. --

※ 发信站: 批踢踢实业坊(ptt.cc) ◆ From: 140.112.218.142