推 dephille:算到讓人很不爽的題目...有整數不出非得要出分數嗎。 11/25 08:25
推 westerveld:第一題...20分!?!?!?!??!?!?!?? 11/26 03:21
課程名稱︰微積分乙
課程性質︰共同必修
課程教師︰康明昌
開課系所︰理、醫、公衛學院
考試時間︰94/11/24
試題 :
(1) Use the formal definition of limits to prove
lim (1/x^2)=1/4
x→2 20%
(2) 1. State Rolle's Theorem and Mean Value Theorem
2. Use Rolle's Theorem to prove Mean Value Theorem 15%
(3) 1. Find the asymptotic lines of y=√(2x^2-x+1)
2. Evaluate lim (1-3/x)^2x
x→-∞
3. Consider the equation x^3+y^3-3xy=0 If
y(4/3)=2/3, find y(2) (4/3) 15%
註：y(2)的(2)是上標 代表y的二次微分
(4) Let f:[0,1]→R be a continuous function and 0≦f(x)≦1
for any xε[0,1] . Show that there is some c satisfying
0≦c≦1 and f(c)=c 20%
(5) Sketch the graph of y=f(x)=2/3(x^3)-2x+1 20%
(6) Let c be a real number which will be determined later. Define
f(x)=3/2(x^4)-2x^3-6x^2+c. Find all the real numbers c such
that f(x)≧0 for any xεR. 20%
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你對，是因為你的事實與推理正確 --Warren buffett
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※ 編輯: greenlibra 來自: 140.112.249.171 (11/25 01:46)