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：
開課系所︰生機、生工、地質、工管
考試日期（年月日）︰2009/11/13
考試時限（分鐘）：8:10~10:00
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
A.(20%)Find the intervals on which f(x) increase and the intervals on which
f(x) decrease.
1.
f(x)={ x+7 , x＜-3
{ |x+1|,-3≦x＜1
{ 5-2x , 1≦x
2.
f(x)={ 4-x^2, x＜1
{ 7-2x ,1≦x＜3
{ 3x-10,3≦x
B.(20%)Find f(x) on the domain indicated given the following information.
1.(0,∞),f'(x)=x^(-5)-5x^(-1/5),and f(1)=0.
2.(-∞,∞),f'(x)=2+sinx,and f(0)=3.
C.(20%)Find the critical points of the function.
f(x)={x^2+2x+2 ,-1/2≦x＜0
{x^2-2x+2 , 0≦x≦2
D.(20%)Determine A and B so that the curve
y=Acos2x+Bsin3x
has a point of inflection at (π/6,5).
E.(20%)Sketch the graph of f(x)=(x^4)/4-2x^2+7/4 on (-5/2,3].
※ 編輯: Rvlyitld 來自: 140.112.202.123 (11/13 10:48)