※ 引述《endlesschaos (土狼)》之銘言：
: ※ 引述《BaBi (迅雷不及掩耳盜鈴)》之銘言：
: : 嗯, 事實上是書上答案和我算出來不太一樣,
: : 還請版友們幫忙看一下是答案寫錯還是我寫錯…
: : (1) Find the derivatives of the following functions
: : f( θ) = sin( θ) where θis measured in degrees.
: : 我的答案是 ( π/ 180 ) sin( πθ/ 180 )
: : 書上給 cos θ...
: 重點在於 f(θ) = sin(θ)
: 你是在對θ做微分
: 自然不會跑出那些替換成徑度的係數
: 倘若今天式子換成 f(x) = sin(x)
: 你也不會去除以 180 吧
我會有疑問主要是因為大一時在 Thomas 的教科書上寫過這題,
題目以題組方式引導式地去解答.
以下節錄一下題目,
(a) With your graphing calculator or computer grapher
in degree mode, graph f(h) = sinh/h and estimate
lim f(h).
h->0
Compare your estimate with π/180. Is there any
reason to believe the limit should be π/180?
(c) Now go back to the derivation of the formula for
the derivative of sin x in the text and carry out
the steps of the derivation using degree-mode limits.
What formula do you obtain for the derivative?
書本後面給的答案便是 (a) π/180
(c) (π/180)(cosx)
補圖 http://i.imgur.com/xuVinwe.png
http://i.imgur.com/f4IKoxV.png
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 36.234.220.163
※ 編輯: BaBi 來自: 36.234.220.163 (02/09 22:14)