課程名稱︰微積分甲下
課程性質︰理工學院必修
課程教師︰官彥良
開課學院：理學院
開課系所︰數學系
考試日期（年月日）︰108.03.07
考試時限（分鐘）：30
試題 :
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.