Re: [考古] 96中興考古

[rygb (再生)]

※ 引述《arebecca455 (sg)》之銘言：
: http://ppt.cc/acxU
: 想請問第7題 第11題
: 第11題讓我想到高中微積分
: 但他沒有給幾次方 我要怎麼設呢？
: 希望大家可以幫我解惑  謝謝

7.
Use integral by Parts

                1                1
∫xf''(2x)dx = --- ∫xdf'(2x) = ----[f'(2x)x - ∫f'(2x)dx]
                2                2

                1               1
             = ---- f'(2x)x - ---- f(2x) + c
                2               4


and put the bound into above. f(0) = 1 ,f(2) = 4 , f'(2) = 5

get the answer 7/4.


11.
     -1
x = f  (y)   ->  y = f(x)

                     -1
and we want to know f  (y) differntial to y =?

             -1
so from x = f  (y)  , we differntial both side respect to x.

      -1
    df  (y)       dy                       dy
   --------  *  ----- = 1     and we know ---- = f'(x)
      dy          dx                       dx

(chain rule)

so if we differential with respect to x again and again , we get the answer.
  2 -1
 d f (y)           -f''(x)
-------- f'(x) = -----------     ,
     2              '    2
   dy             [f (x)]

                               2
  -1    '''           3[f''(x)]       -f'''(x)
[f  (y)]    f'(x) =  -----------  +  ---------  and put the condition.
                             4              3
                     [f'(x) ]        [f'(x)]


f(1)=4  imply x = 1 , y=4

  -1     '''
[f  (4)]     = -3/32








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◆ From: 114.34.122.244
→ dali510313:那個...我的第11題跟你不一樣說= =
→ rygb:真的假的 我檢查一下好了
※ 編輯: rygb            來自: 114.34.122.244       (06/26 20:34)
推 dali510313:對了!!!:)
→ dali510313:推r大的過程阿!!!!我都不會打Q_Q
→ rygb:感謝你 :D
→ arebecca455:謝謝r大！！我要再去把觀念弄清楚了
→ arebecca455:謝謝你們