作者LuisSantos (^______^)
看板trans_math
標題Re: [微分]
時間Thu Jan 25 02:08:43 2007
※ 引述《king911015 (早已放棄愛上你)》之銘言：
: For what value or values of the constant K will the curve
: y=X^3+kX^2+3X-4 have exactly one horizontal tangent?
: Suppose a,b are constants such that lim sin2x a
: x->0 (------- + ---- + b )=0
: x^3 x^2
: then a+b =?
sin2x a
lim (------- + ----- + b)
x->0 x^3 x^2
sin2x + ax + (b)(x^3)
= lim (-----------------------)
x->0 x^3
(2)(cos2x) + a + (3b)(x^2)
= lim (-----------------------------) --------(＊)
x->0 3x^2
sin2x a
因為 lim (------- + ----- + b) = 0
x->0 x^3 x^2
所以 (2)(cos0) + a + (3b)(0) = 0
2 + a = 0 => a = -2 代入(＊)
(2)(cos2x) - 2 + (3b)(x^2)
lim (----------------------------)
x->0 3x^2
(-4)(sin2x) + (6b)(x)
= lim (-----------------------)
x->0 6x
(-8)(cos2x) + 6b
= lim (-------------------)
x->0 6
-8 + 6b
= --------- = 0
6
8 4
-8 + 6b = 0 => 6b = 8 => b = --- = ---
6 3
4 -6 + 4 -2
a + b = -2 + --- = -------- = ----
3 3 3
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