[試題] 96暑 周青松 微積分上期中考

[mario1986 (馬力歐)]

課程名稱︰微積分甲上
課程性質︰
課程教師︰周青松
開課學院：
開課系所︰
考試日期（年月日）︰2008/7/14
考試時限（分鐘）：
是否需發放獎勵金：是
（如未明確表示，則不予發放）

試題 :

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

                       (每大題均20分)

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◆ From: 140.112.244.218
※ 編輯: mario1986       來自: 140.112.244.218      (07/14 14:00)
※ 編輯: mario1986       來自: 140.112.244.218      (07/14 14:00)
推 Oldfather75:op
推 asuralee:沒OP吧@@
推 imxp:這是今年7/14才考的內...
推 tomroy:樓上學長考100被點名還沒有到哈哈
推 imxp:你怎麼知道
推 friendlysam:就是他　100分學長!!
→ imxp:是不是發生了什麼事情我不知道??
推 flypig7882:是的 學長被點名了
推 imxp:可以多說一點嘛 好刺激喔
推 geosheep:GOOD　原來那就是你XD