作者LuisSantos (^______^)
看板trans_math
標題Re: [微分] 台聯大95第一題
時間Sat Feb 24 00:18:31 2007
※ 引述《handsamjoy (真*鄉民無雙)》之銘言：
: 9x-3sin3x
: ------------
: f(x)= 5x^3 ,x不等於0
: a ,x=0
: If the function f is continous on the entire real line Then a=?????
Since the function f is continuous on the entire real line ,
lim f(x) = f(0) = a
x→0
lim f(x)
x→0
9x - 3sin3x 0
= lim ------------- (---)
x→0 5x^3 0
9 - 9cos3x 0
= lim ------------ (---)
x→0 15x^2 0
27sin3x 0
= lim --------- (---)
x→0 30x 0
81cos3x 81 27
= lim --------- = ---- = ---- = a
x→0 30 30 10
27
所以 a = ----
10
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