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）︰2014/11/25
考试时限（分钟）：40
试题 :
1. (10%) Assume that f has a derivative which is monotonic decreasing and
satisfies f'(x) ≧ m > 0 for all x ∈ [a, b]. Prove that the integral
b
∫ cos f(x) dx
a
is bounded by a constant only depending on m.
2. (10%) Let a = 3 and
1
3 (1+a )
n
a = ────, n = 1, 2, ...
n+1 3 + a
n
＿
Show that a → √3.
n