[試題] 95暑 周青松 微積分上期中考

[meiandnsync (我想打好球)]

課程名稱︰ 微積分上
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）︰ 2007/7/中旬
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=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]


--
※ 發信站: 批踢踢實業坊(ptt.cc) 
◆ From: 125.230.76.201
推 yeti:小嫩~~~   >///<