課程名稱︰微積分甲
課程性質︰
課程教師︰周青松
開課系所︰數學系
考試時間︰2006年7月26日
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
I. Sketch the graph of the function f(x) = 1/4x^4 - 2x^2 + 7/4 on [-5,5]
II. Assume that f is a continuous function and that
x
∫tf(t)dt = sinx - xcosx
0
A). Determine f(π/2).
B). Find f'(x).
III. Let { 1-x^2, -1≦x≦1 x
f(x) ={ 1, 1≦x≦3 and let g(x)=∫f(t)dt
{ 2x-5, 3≦x≦5 -1
A). Carry out the integration.
B). Sketch the graph of f and g.
IV.
A). Find f given that f''(x)=6x-2,f'(1)=-5,and f(1)=3.
B). Find f given that f''(x)=sinx,f'(O)=-2,f(0)=1.
V.
d 2x
A). Calculate the derivative ─(∫ t√(1+t^2) dt)
dx tanx
B). Find H'(3) given that
1 x
H(x) = ─∫[2t-3H'(t)]dt
x 3
(每大題均20分)
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