[微積分]考古題
九六期末第三題的B
B) Let f'(x) = kf(x) for all x in some interval.
Prove that f(x) = Ce^kx ,
where C is an arbitrary constant.
兩個證明方法
(M1) set f(x)=ce^kx
=> f'(x)=kce^kx=k*f(x)
(M2) 這題其實是Seperable ODE
set y=f'(x)
we can rewrite the equation as follow
dy
---- = k y
dx
seperate x y
dy
---- = k dx
y
intergrate both sides
ln y = kx + C
=> y= e^(kx+C) = e^kx * e^C = C' e^kx
(((C'=e^c)))
然後cross section perpendicular to the x-axis就是截面積跟x軸垂直
繞著X軸旋轉的意思
以上
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 220.132.83.187
推
01/08 14:50, , 1F
01/08 14:50, 1F
討論串 (同標題文章)
完整討論串 (本文為第 2 之 2 篇)：