作者unmolk (UJ)
看板NTU-Exam
标题[试题] 107-2 官彦良 微积分甲下 小考一
时间Wed Mar 27 17:25:45 2019
课程名称︰微积分甲下
课程性质︰理工学院必修
课程教师︰官彦良
开课学院：理学院
开课系所︰数学系
考试日期（年月日）︰108.03.07
考试时限（分钟）：30
试题 :
1. Let C be a curve with parametric equations x = sint and y = cost + ln(csct
- cost), where 0 < t < π.
(a)(20%) Find the slope of the tangent line at a point P = (x(t0),y(t0)) of C
(b)(10%) Compute the arc length of C from t = π/3 to t = 2π/3
10
2. (20%) Find ∫x^2/(1+x^2) dx.
0
3. Let r(t) = <cost, sint, lncost> and P = (1,0,0).
(a)(30%) Find the unit tangent vector T, the normal vector N and the binormal
vector B of r(t) at P.
(b)(20%) Find the normal plane and the osculating plane of r(t) at P.
--
※ 发信站: 批踢踢实业坊(ptt.cc), 来自: 140.112.25.3
※ 文章网址: https://webptt.com/cn.aspx?n=bbs/NTU-Exam/M.1553678751.A.D62.html