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Anonymous
Anonymous asked in 科學數學 · 1 decade ago

拜託幫解幾題微積分

我把題目放在相本上

麻煩連一下黑

這樣題目比較清楚

http://photo.xuite.net/h20021019/3131486/2.jpg

Update:

原來linch大師以前有算過了

第2題跟第1題看起來很像

就差在一各是(x:1~∞)另一各是(x:0~1)

但是覺得答案會差很多

Update 2:

請問他的上下限有差嗎??

1 Answer

Rating
  • linch
    Lv 7
    1 decade ago
    Favorite Answer

    第一題請見

    http://tw.knowledge.yahoo.com/question/question?qi...

    2009-03-18 12:39:15 補充:

    第二題答案相反

    if p<1 converges, if p>=1 diverges.

    2009-03-27 15:03:10 補充:

    疑那個連結題目不一樣了嗎?

    1. Let f(x) = √x, f'(x) = 1/(2√x), f(49) = 7, f'(49) = 1/14

    所以函數在 x = 49 的線性化為 f(49) + f'(49)(x - 49) = 7 + (x - 49)/14

    因此 √48 ≒ 7 + (48 - 49)/14 = 7 - 1/14 ≒ 6.928

    (√48 = 6.9282 ...... )

    2. 以前算過找出來給你看

    圖片參考:http://i580.photobucket.com/albums/ss244/linch_1/p...

    3. f(x, y) = - 6xy^2 + 2x^3 + 3y^4 + 2

    f_x (x,y) = - 6y^2 + 6x^2, f_y (x,y) = - 12xy + 12y^3

    f_x (x, y) = 0 and f_y (x, y) = 0 ==> (x, y) = (0, 0) or (1, 1)

    (0, 0), (1, 1) are critical points.

    4. x^4 + y^4 = 2xy 兩邊對 x 微分 ( 隱微分 )

    4x^3 + 4y^3 y' = 2y + 2xy' ==> y' = (4x^3 - 2y) / (2x - 4y^3)

    在 (1, 1) 處 y' = - 1 ( 把 x = 1, y = 1 代入上式 )

    所以切線為 y - 1 = - (x - 1)

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