[試題] 周青松 微積分甲上（2005秋 期中考）

[Nzing (黑色神話)]

課程名稱︰微積分甲
課程性質︰共同必修
課程教師︰周青松
開課系所︰數學系
考試時間︰2005.11.11 8:10~10:00

試題 :
Ⅰ.Show that

        sin x
A. lim ─── = 1
   x→0   x

        1-cos x
B. lim ──── = 0
   x→0    x


Ⅱ.
A. Determine the discontinuites, if any , on the following function:

               {  2x+1 , x≦0
        f(x) = {     1 , 0＜x≦1
               { x^2+1 , x＞1

B. Given that

             {  x^2 , x≦1
        f(x)={
             { 2x-1 , x＞1

   find f'(1)

Ⅲ.Let f be continuous on an arbitrary interval I and differentiable on
   the interior of I.
A. If f'(x)＞0 for all x in the interior of I,
   then f increase on all of I

B. If f'(x) = 0 for all x in the interior of I, then f is constant
   on all of I.

Ⅳ. Let f be twice differentiable on an open interval O 屬於 R
A. If f''(x)＞0 for all x in O, then the graph of f is concave up.

B. If f''(x)＜0 for all x in O, then the graph of f is concave down.

                                              4     2
Ⅴ.Sketch the graph of the function f(x)=1/4 x  - 2x + 7/4

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※ unicorn999:轉錄至看板 NTUBIME99-HW                              10/30 23:57
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