作者danco (danco)
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标题[试题] 99上 王金龙 微积分甲上 第四次小考
时间Sun Nov 14 20:43:34 2010
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）：2010/10/14
考试时限（分钟）：30 mins
是否需发放奖励金：是
（如未明确表示，则不予发放)
A. (10 points) Suppose that f : R → R is continuous and
x
let F(x) = ∫ f(t)dt. Show that F'(x) = f(x) for all x ∈ R.
0
B. (10 points) Suppose that f : R → R is dierentiable at x = a and f(a) is
a maximum of f. Show that f'(a) = 0.
C. (10 points) Suppose that f : R → R is dierentiable on (a-δ,a)∪(a,a+δ)
for some δ > 0. "continuous at x = a" and lim f'(a) = L. Show that f'(a)
exists and equals to L. x→a
x≠a
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1F：推 yuyumagic424:differentiable 11/15 20:15