作者mario1986 (马力欧)
看板NTU-Exam
标题[试题] 96暑 周青松 微积分上期中考
时间Mon Jul 14 13:58:54 2008
课程名称︰微积分甲上
课程性质︰
课程教师︰周青松
开课学院:
开课系所︰
考试日期(年月日)︰2008/7/14
考试时限(分钟):
是否需发放奖励金:是
(如未明确表示,则不予发放)
试题 :
1.
A). Give necessary and sufficient condition on A and B for the function
{ Ax-B , x≦1
f(x) ={ 3x , 1<x<2
{Bx^2-A , 2≦x
to be continuous at x=2 but discontinuous at x=1.
2. Show that:
A). Sin x
lim ──── = 1
x→0 x .
B). 1-cos x
lim ──── = 0
x→0 x .
3.
A). Find C and D given that the function
f(x) ={ x^2-2 , x≦2
{D(x^2)+Cx , x>2
is differentiable at x=2.
B). Find C and D given that the derivative of
f(x) ={C(x^3)+Dx+2 , x≦2
{D(x^2)-C , x>2
is everywhere continuous.
4. Assume that f and g are differentiable on (-c,c), c>0 and f(0)=g(0).
A). Show that if f'(x)>g'(x) for all x∈(0,c),
then f(x)>g(x) for all x∈(0,c).
B). Show that if f'(x)>g'(x) for all x∈(-c,0),
then f(x)<g(x) for all x∈(-c,0).
5.
A). Determine C and D so that the curve
y = C cos2x + D sin 3x
π
has a point of inflection at (── , 5 )
6
B). Sketch the graph of the function
1 3
f(x) = ──(x^3 - ──x^2 - 6x + 2) on [-2,∞).
4 2
(每大题均20分)
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※ 编辑: mario1986 来自: 140.112.244.218 (07/14 14:00)
※ 编辑: mario1986 来自: 140.112.244.218 (07/14 14:00)
1F:推 Oldfather75:op 07/21 17:21
2F:推 asuralee:没OP吧@@ 07/21 17:31
3F:推 imxp:这是今年7/14才考的内... 07/22 14:01
4F:推 tomroy:楼上学长考100被点名还没有到哈哈 07/23 15:18
5F:推 imxp:你怎麽知道 07/30 00:14
6F:推 friendlysam:就是他 100分学长!! 07/31 21:05
7F:→ imxp:是不是发生了什麽事情我不知道?? 08/01 17:05
8F:推 flypig7882:是的 学长被点名了 08/06 21:58
9F:推 imxp:可以多说一点嘛 好刺激喔 08/14 00:11
10F:推 geosheep:GOOD 原来那就是你XD 08/15 23:41