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）︰2014/11/03
考試時限（分鐘）：1HR
試題 :
1. Complete the following limits:
＿＿＿＿＿
√1-cos(ax)
(a) lim ────── , where a, b are constants.
x→0- sin(bx)
１
(b) lim cos(x) ^ (─────)
x→0 1- cos(2x)
1 １
(c) lim ──── - ────
x→0 sinh(x) e^x -1
2. Complete the following derivatives.
π dy｜
(a) arctan(xy) + arccos(x+y) = ─ . Find ─｜ .
３ dx｜(0,½)
dy
(b) y=sec(x) ^ log sinh(x) . Find ─ .
2 dx
dy
(c) y=arccosh[sec(√x)]. Find ─ .
dx
3. f(x) = ln｜ln(x)-1｜.
(a) Find the domain of f.
(b) Find the vertical asymptotes of f.
(c) Find the intervals of increase or decrease.
(d) Find the intervals of concativity and the inflection points.
(e) Sketch the graph of f.