作者NTUkobe (台大科比)
看板NTU-Exam
標題[試題] 102上 林楨芸 微積分甲上 第七次小考
時間Fri Jan 17 17:48:54 2014
課程名稱︰微積分甲上
課程性質︰必修
課程教師︰林楨芸
開課學院：理學院
開課系所︰數學系
考試日期（年月日）︰102/11/18
考試時限（分鐘）：20分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
CALCULUS A-QUIZ 7 NAME:____________
Problem 1. Make a sketch of the region on the xy-plane consisting of all
1 2
points (x,y) satisfying 0 < = x < = 2, ---x < = y < = x. Compute the volume of
2
the solid obtained by rotating this region about the horizontal line passing
through (0,3). (6 points) ("< =" 代表 "小於等於")
Problem 2. Find the volume common to two circular cylinders, each with radius
r, if the axes of the cylinders intersect at right angles. (7 points)
Problem 3. Sketch the region in the xy-plane defined by the inequalities
x-y > = 0, 3-x-2│y│ > = 0 and find its area. (7 points)
Answers:
12π 4√2π
Problem 1. : ----- - -------
5 3
16r^3
Problem 2. : -----
3
10
Problem 3. : ----
3
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