作者wheata (仙人指路不用钱)
看板NTU-Exam
标题[试题] 99上 王金龙 微积分甲上 第六次小考
时间Thu May 26 20:23:11 2011
课程名称︰微积分甲上
课程性质︰必修
课程教师︰王金龙
开课学院：理学院
开课系所︰数学系
考试日期（年月日）︰2010/10/28
考试时限（分钟）：30
是否需发放奖励金：是
（如未明确表示，则不予发放）
试题 :
1
A. (5 points) Evaluate∫ [(x/(1+x))^(1/2)] dx
0
┌ x^(2x) if x > 0
B. Let f(x) = │
└ 1 if x = 0
(a) (5 points) Show that lim f(x) exists and f is continuous at x = 0.
x→0
x≠0
(b) (5 points) Find all relative extrema of f.
(c) (5 points) Find all points of inflection of f if there is any.
┌ (x^2)sin(1/x) if x ≠ 0
C. Let f(x) = │
└ 0 if x = 0
(a) (5 points) Show that f is differentiable at x = 0 and find f'(0).
(b) (5 points) Find f'(x) for all x. Is f'(x) continuous?
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