課程名稱︰微積分甲上
課程性質︰必修
課程教師︰周青松
開課學院：理學院
開課系所︰數學系
考試日期（年月日）︰2014.7.16
考試時限（分鐘）：50
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
(1) Find f from the information given: (20pt)
f''(x)=cosx, f'(0)=1, f(0)=2.
(2) Evaluate the integrals
(a) ∫3π/2 f(x)dx, where f(x)= 2sinx , 0≦x≦π/2
0 2+cosx , π/2<x≦3π/2 .(20pt)
(b) ∫π/4 (x^2-2x+sinx+cos2x)dx.(20pt)
-π/4
(3) Let f be a continuous function, c a real number. Show that (20pt)
∫b+c f(x-c)dx=∫b f(x)dx.
a+c a
(4) Let F(x)=∫x t(t-3)^2 dt.
0
(a) Find the critical points for F and determine the intervals on which
F increases and the intervals on which F decreases.
(b) Determine the concavity of the graph of F and find the points of
inflection, if any.
(c) Sketch the graph of F.