課程名稱︰分析導論優二
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）︰2015/04/14
考試時限（分鐘）：20
試題 :
n
1. (10%) (i) Let E be a Jordan region in |R and f : E → |R be integrable on E.
k
If f → f uniformly on E as k → ∞, prove that f is integrable on E and
k
lim ∫ f dx = ∫ f dx.
k→∞ E k E
(ii) Prove that
x y
lim ∬ cos(-) exp(-) dA
k→∞ E k k
2
exists and find its value for any Jordan region E in |R .