[試題] 99上 王金龍 微積分甲上 第四次小考
課程名稱：微積分甲上
課程性質：必修
課程教師：王金龍
開課學院：理學院
開課系所：數學系
考試日期（年月日）：2010/10/14
考試時限（分鐘）：30 mins
是否需發放獎勵金：是
（如未明確表示，則不予發放)
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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11/15 20:15, , 1F
11/15 20:15, 1F