作者chaochienyao (yao)
看板NTUBIME100HW
標題[轉錄][試題] 93年暑修 周青松微積分甲上期末考
時間Sat Dec 15 17:12:55 2007
※ [本文轉錄自 NTU-Exam 看板]
作者: cmTing ( ~Eyes On Me~ ) 看板: NTU-Exam
標題: [試題] 93年暑修 周青松微積分甲上期末考
時間: Mon Jul 25 01:01:47 2005
課程名稱︰微積分甲
課程性質︰必修
課程教師︰周青松
開課系所︰數學系
考試時間︰2004.07.26
試題 :
2004.07.26
Ⅰ.(A)Find the critical numbers and chasify all extreme values of the function
2
f(X) = X - 2｜X｜+ 2
3 2
(B)Find the point of inflection for the function f(X) = X - 6X + 9X + 1
2
Ⅱ. ┌ 1 - X , -1 < X < 1 x
Let 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
Ⅲ.(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'(0) = -2 , and f(0) = 1
2x 2
Ⅳ.(A)Let H(X) = ∫ dt/1+t , find H'(X)
x
x
(B)Let H(X) = 1/X ∫ [ 2t-3H'(t)] dt , find H'(3)
3
2/3
Ⅴ.(A)Let Ω be the region bounded below by the curve y = X + 1 , bounded
to the left by the y-axis , and bounded above by the line y = 5. Find the
volume of the solid generated by revolving Ω about the y-axis.
(B)Find the volume of the solid generated by revolving the region between
2
y = X and y = 2X about the X-axis.
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