作者meiandnsync (我想打好球)
看板NTU-Exam
标题[试题] 95暑 周青松 微积分上期中考
时间Sat Jul 12 19:55:23 2008
课程名称︰ 微积分上
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)︰ 2007/7/中旬
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=1 but dis continuous at x=2.
B). Find A and B given that the function
f(x) ={x^3 , x≦1
{Ax+B , x>1
is differentiable at x=1.
2.
A). Show that
Sin x 1-cos x
lim ──── = 1 and lim ──── = 0
x→0 x x→0 x
B). Find A and B given that the derivative of
{ Ax^2+B x<-1
f(x) = { Bx^5+AX+4 x>=-1
is everywhere continuous
3.
A). Let f and g be differentiable functions such that f'(x)=g(x) and
g'(x)=f(x), and let H(x)=[f(x)]^2-[g(x)]^2.
Find H'(x).
B). Find the indicated derivative:
d
─[Sin(f(3x))] when f differentiable
dx
4.
A). Find f given that f'(x)=6x^2-7x-5 for all real x and f(2)=1
π π
B). Set f(x)=sec^2 x and g(x)=tan^2 x on the interval (-─ , ─)
π π 2 2
Show that f'(x)=g'(x) for all x in (-─ , ─)
2 2
5. Sketch the graph of the function f(x) = 1/4x^4 - 2x^2 + 7/4 on [-3,3]
--
※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 125.230.76.201
1F:推 yeti:小嫩~~~ >///< 07/16 15:41
※ TameFoxx:转录至看板 b982040XX 11/11 18:24