課程名稱︰分析導論優一
課程性質︰數學系大二必修
課程教師︰王振男
開課學院：理學院
開課系所︰數學系
考試日期（年月日）︰2014/11/25
考試時限（分鐘）：40
試題 :
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