課程名稱︰微積分甲上
課程性質︰必修
課程教師︰蔡雅如
開課學院：電資學院 工學院
開課系所︰電機系 材料工程系 資工系 資管系
考試日期（年月日）︰2010/10/11
考試時限（分鐘）：45分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.Calculate the following limits.
(a) lim {√(x^2+ax)- √(x^2+bx)}, where a,b are constants.
x→-∞
1
sinx‧cos--- x>0
(b) lim f(x),where f(x)= x
x→0
x
--- x<0
[x]
([x] is the greatest integer funtion)
x^2, if x is irrational
2.f(x)=
0 , if x is rational
(a) At which number is f continuous?
,
(b) At which number is f differentiable? What is f(x)?
3.Difine functions of a∈R , f(a) and g(a), by the equations:
-1 e^x-1 -1 e^x-1
f(a)=lim tan (-------) and g(a)=lim _ tan (-------)
x→0 │x│^a x→0 │x│^a
(a) Find the domains of f(a)and g(a).
(i.e for what values of a do the above limits exist ?)
(b) Compute g(a) for all a in its domains, At which number is g discontinuous?
e^x-1
(Hint: lim (-------)=1)
x→0 x
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◆ From: 140.112.240.113
※ 編輯: FAlin 來自: 140.112.240.113 (10/18 20:16)