作者  cmTing (  ~Eyes On Me~  )                               看板  NTU-Exam 
 標題  [試題] 93年暑修 周青松微積分甲上期末考                                 
 時間  Mon Jul 25 01:01:47 2005                                               
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課程名稱︰微積分甲
課程性質︰必修
課程教師︰周青松
開課系所︰數學系
考試時間︰2004.07.26

試題 :

  2004.07.26

Ⅰ.(A)Find the critical numbers and chasify all extreme values of the function
           2
   f(X) = X - 2｜X｜+ 2
                                                            3    2
   (B)Find the point of inflection for the function f(X) = X - 6X + 9X + 1
                      2
Ⅱ.           ┌ 1 - X  , -1 < X < 1                   x
   Let f(X) = ├ 1      ,  1 < X < 3  and let g(X) = ∫  f(t)dt
              └ 2X - 5 ,  3 < X < 5                   1

   (A)Carry out the integration

Ⅲ.(A)Find f given that f"(X) = 6X - 2 , f'(1) = -5 , and f(1) = 3
   (B)Find f given that f"(X) = sinX   , f'(0) = -2 , and f(0) = 1

                   2x      2
Ⅳ.(A)Let H(X) = ∫   dt/1+t , find H'(X)
                    x
                       x
   (B)Let H(X) = 1/X ∫  [ 2t-3H'(t)] dt , find H'(3)
                       3
                                                           2/3
Ⅴ.(A)Let Ω be the region bounded below by the curve y = X   + 1 , bounded
   to the left by the y-axis , and bounded above by the line y = 5. Find the
   volume of the solid generated by revolving Ω about the y-axis.

   (B)Find the volume of the solid generated by revolving the region between
        2
   y = X  and y = 2X about the X-axis.