[情報] 給沒有微積分題目的人

[lightcloud (hdhd)]

34.The dial of a standard clock has a 10-centimeter radius.

   One end of an elastic string is attached to the rim at 12

   and the order to the tip of the 10-centimeter minute hand.

   At what rate is the string stretching at 12:15(assuming that

   the clock is not slowed down by this stretching) ?

36.
             ︴x^2 sin 1/x  if x ≠ 0
   Let f(x)= ︴
             ︴0            if x = 0

   (a) Find f'(x) for  x ≠ 0 by using derivative.

   (b) Find f'(0) from the definition of the derivative.

   (c) Show that f'(x) is discontinuous at x=0

40.

   Suppose that f is a differentiable function

     (a) Find   d/dx f(f(x))

     (b) Find   d/dx f(f(f(x)))

     (c) Find   d/dx f(f(f(f(x)))

     (d) Let f[n] denote the function defined as follows:f[1]=f and
         f[n]=f。f[n-1] for n>=2.Thus,f[2]=f。f,f[3]=f。f。f, and so
         on.Based on your results from parts (a) through (c),make a
         conjecture regarding d/dx f[n](x). Prove your conjecture.


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◆ From: 140.128.68.250
→ wellcomes:學弟你做的太好了！像我們M48通常都是PO答案啦...XD
推 santta:大推!
推 rrichard:對阿...害我每次想寫的時候都有答案了XD 所以從來沒寫過.
推 ckTodd:嗯嗯…組頭，照學長說的做吧！
推 timchenegg:36題是否為  Let f(x)=0  if x=0 ?
※ 編輯: lightcloud      來自: 140.128.68.250       (10/05 19:52)
推 yiling0917:感恩阿...
推 ahkeithn:36題應為: (a) -cos 1/x + 2x sin 1/x
→ ahkeithn:(b) lim(f(0+x)-f(0))/x = lim(f(x)-f(0))/x = x sin 1/x
→ ahkeithn:    上面打錯,最後應是 lim x sin 1/x = 0
→ ahkeithn:(c) 因 lim f'(x) = lim (-cos1/x+2xsin1/x) 不存在,
→ ahkeithn:    (lim cos 1/x 不存在),f'(x) cannot be continuous
→ ahkeithn:    at x=0, 雖然 f'(0) 存在
→ ahkeithn:注意: lim 下面有 x->0,因此推文版面有限
推 magiccats:這玩意是啥時要交阿?
推 hyhk:有沒有中文翻譯~~XDD
推 t19990517:每個英文字母都看的懂 拼起來就看不懂了 囧
推 zerofeather:ㄎ~~~真是難得~~辛苦了!