课程名称︰分析导论优二
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）︰2015/04/14
考试时限（分钟）：20
试题 :
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 .