数理经济小组&微积分助教小组
江西财经大学国际学院
2014 级微积分期末复习试卷(A )
——By 程伟婷&叶煜
From 微积分助教组
1. Full in the blank of each statement in the following five statements such that the
statement is right. Then write the corresponding answer on the answer book by the title
number. You can be gained 3 points for the right thing on per blank.
(1)
(2)
(3)
(4)
=__________.
(5)
=____________.
2. Choose the one that the statement is right from four choices marked A, B, C, and D,
with which each statement of the following five statements. Then write the
corresponding answer on the answer book by the title number. You can be gained 3
points for the right choice of per the statement.
(6)
(
).
(A)
(B)
(C)
(D)
(7)If
,then the values of a and b are ( ).
(A) a=-8,b=2;
(B)a=2,b is arbitrary;
(C) a=2,b=-8;
(D) Both a and b are arbitrary.
(8) If f(x) is continuous, and
number, then (
).
, C is any constant
（A）
(B)
(C)
;
;
;
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数理经济小组&微积分助教小组
(D)
.
(9) If f(x) is differentiable, then
(A) 2x
(B)2x
(10) If I=
_________.
; (C)
then I=(
(A) –(
(B)
(C) (
（D）-
;(D)
.
).
;
.
3. Give the solution of any of in the following problems and write operation process and
answer on the answer book by the title number. You can be gained mark of per problem
by the right process and answer.
(11)
(12) Find f (x), if f(x)=
(13)
(14) Given that f(x)=
(1) Find the intervals on which f(x) is increasing or decreasing.
(2) Find the local maximum and minimum values of f(x).
(3) Find the intervals of concavity and the inflection points.
(4) Find asymptote lines of the curve y=f(x).
(15) Determine the production level that will maximize the profit for a
company with cost and demand functions.
C(x)=1450+36x-
p(x)=60-0.01x
(16) Use the method of cylindrical shells to find the volume of the solid
obtained by rotating the region bounded by the given curves about the
x-axis.
X=4
x=0
(17)State the concavity test theorem and prove it.
(18) Let f(x) be continuous on [0,2], differentiable on (0，2). If f(2)=0, then
for every real R there is at least one number c in (0,2) for which
Rf(c)+cf (c)=0.
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