课程名称︰分析导论优一
课程性质︰数学系大二必修
课程教师︰王振男
开课学院：理学院
开课系所︰数学系
考试日期（年月日）︰2014/11/04
考试时限（分钟）：40
试题 :
1. (10%) Let h be a fixed positive number. Show that there is no function f
satisfying the following three conditions: f'(x) exists for x ≧ 0, f'(0) =
0, and f'(x) ≧ h for x > 0.
2. (10%) Let f be a real-valued function on [0, 1]. Assume that f(0) > 0, f(x)
≠ x for all x, and f(x) ≦ f(y) whenever x ≦ y. Let A = {x: f(x) > x}. Show
that sup A ∈ A and that f(1) > 1.