作者NTUkobe (台大科比)
看板NTU-Exam
标题[试题] 102上 林桢芸 微积分甲上 第七次小考
时间Fri Jan 17 17:48:54 2014
课程名称︰微积分甲上
课程性质︰必修
课程教师︰林桢芸
开课学院：理学院
开课系所︰数学系
考试日期（年月日）︰102/11/18
考试时限（分钟）：20分钟
是否需发放奖励金：是
（如未明确表示，则不予发放）
试题 :
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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