課程名稱︰微積分甲上
課程性質︰大一必修
課程教師︰蔡雅如
開課學院：電資院、管理院、社科院
開課系所︰資工系、資管系、經濟系
考試日期（年月日）︰2014/12/01
考試時限（分鐘）：1HR
試題 :
1. Evaluate the following limits:
ｎ １ 4i
(a) lim Σ ─ ───────
n→∞ i＝1 ｎ √[n^2 + 4i^2]
１ 1-cos(x) ＿＿＿
(b) lim ── ∫ √2+t^2 dt
x→0 ｘ^2 -x^2
2. Evaluate the following indefinite integrals.
3
(a) ∫{ln[1+sin(x)]}cos (x) dx
3 ⅓
(b) ∫tan (x)‧sec (x) dx
2
(c) ∫x arccos(x) dx
3.Let R be the region bounded by x＝4y^2 - y^3 and x＝0 .
(a) Find the volume of the solid obtained by rotating R about the line y＝-1 .
(b) Find the volume of the solid obtained by rotating R about the line x＝-1 .