A. ( f (b) − f (a))( g(b) − g(a)) < 0
B.
f '(x) g '(x) < 0
C. ∫ f (x)dx∫ g(x)dx < 0
b
b
D. ∫a f (x)dx∫a g(x)dx < 0
9) If F (x) is an antiderivative of f (x) , C is any constant, then ____ is correct.
A. F (x) = C∫ f (x)dx
C. F '(x) = f (x) +C
x
∫ B. F (x) = f (x)dx C
D. F (x) = lim f (x + h) − f (x)
h→∞
h
10) a and b are in the domains of f (x) and g(x) , then ___ is correct.
7) If l= im f (x) li= m f '(x) 0, lim f ''(x) ≠ 0 but exists, then ________.
x→a
x→a
x→a
A. lim f (x) = 0, x→a f '(x)
B. lim f (x) ≠ 0 but exists, x→a f '(x)
C. lim f (x) = ∞, x→a f '(x)
D. lim f (x) ≠ ∞ but does not exist. x→a f '(x)
8) If f (x) is a continuous on interval [a,b], then in [a,b], f (x) at least have_ __
A. lim ( f (x)g(x)) = lim f (x) lim g(x)
x→a
x→a
x→a
B. ( f (x)g(x)) ' = f '(x)g '(x)
b
b
b
C. ∫ f (x)g(x)dx = ∫ f (x)dx∫ g(x)dx
∫D. a
f (x)g(x)dx = ∫a
f (x)dx∫a
3) The inverse function of =y 2x −1 + 5 is ______________________________. 4) Suppose f (x) is differentiable, then the value of f (x) at x = a is______, and
( ) 4) d ex tan x = dx
of this function is _________________. sin x
2) The discontinuous point of ex −1 is _________________________.
5)
d x −1 dx x2 +1 x=0 =
g ( x)dx
2008-2009 学年第一学期《高等数学 D（英语）》期末考试试卷（A 卷）--2
2. Fill in the blanks (10 marks)
1)
The domain of the function
log 3
2x x −1
is ________________ and the region
1. Choose a right answer of four to the following questions (10 marks) 1) For the following concepts of a function, _____ is not relative to a limitation
4) lim f (x) exists, then ___________ x→a+
A. lim f (x) = f (a) (a+ ) x→a+
C. lim f (x) = lim f (a)
x→a+
x→a
D. none is A. B. C..
5) If f (x), g(x) are differentiable in [a,b], where f (x)g(x) < 0 , then _______
A. a critical point. C. an absolute maximum point.
B. a stationary point. D. an inflection point.
3) If f (x) is a bounded function defined on [a,b], then f (x) must be ___ A. continuous B. differentiable C. integrable D. increasing
A. f (c)= b − a
B. f '(c)= b − a
C. lim f (x)= b − a x→c
∫ D.
1
b
f (x)dx= b − a
f (c) a
此卷选为：期中考试( )、期终考试( √ )、重考( )试卷
年级 专业 题号 一
学号
二
三
姓名
四
五
任课教师 总分
得分
（注意：本试卷共 5 大题，3 大张，满分 100 分．考试时间为 120 分钟。要求写出解题过程，否则不予计分）
2008-2009 学年第一学期《高等数学 D（英语）》期末考试试卷（A 卷）--1
同济大学课程考核试卷（A 卷）
2010—2011 学年第一学期
命题教师签名：梁进
审核教师签名：
课号：122008
课名：高等数学 D（英语） 考试考查：考试
6) If f (x) is an integrable function, then there exists c ∈ (a,b) , such that__
A. continuity B. derivative C. integration D. variable
2) If a,b are in the domain of a decreasing function f (x) , and a < b , then ___
A. f (a) ≤ f (b) B. f (a) ≥ f (b) C. f (a) = f (b) D. f (a) ≈ f (b)