课程名称︰微积分甲上
课程性质︰大一必修
课程教师︰蔡雅如
开课学院：电资院、管理院、社科院
开课系所︰资工系、资管系、经济系
考试日期（年月日）︰2014/11/03
考试时限（分钟）：1HR
试题 :
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.