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.