阿摩線上測驗
題組內容
3. (15%) Let f be continuous on [a, b].
(a) (10%) Then, the function F defined on [a, b] by F(x) =
f(t)dt is continuous on [a, b] and differentiable on (a, b). Prove that F'(x) = f(x) for all x in (a, b). Hint: F(x+h)-F(x) 
f(x) × h if h is small enough. (圖示證明(pictorial proof)即可)
f(t)dt is continuous on [a, b] and differentiable on (a, b). Prove that F'(x) = f(x) for all x in (a, b). Hint: F(x+h)-F(x) f(x) × h if h is small enough. (圖示證明(pictorial proof)即可)