作者BaBi (迅雷不及掩耳盜鈴)
看板trans_math
標題Re: [微分]彰師考古題
時間Fri Jan 4 16:52:04 2013
※ 引述《RAIN2012 (可愛又迷人的反派角色)》之銘言：
: (跪拜高手。)
: Find the limits
: 1. lim X^1/2 * lnX
: x→0+
lnx -∞
lim (√x)(lnx) = lim ------------ [ --- type ]
x->0+ x->0+ x^(-1/2) ∞
L' (1/x)
= lim ------------------
x->0+ (-1/2)[x^(-3/2)]
= lim (-2)(√x)
x->0+
= 0
: 因為沒有解答，所以想詢問是否算對？
: 2.
: 1 1
: lim [ ----- - ----- ]
: X→1+ X-1 lnX
1 1 (lnx)-(x-1) 0
lim ( ----- - ----- ) = lim ------------ [ --- type ]
x->1+ x-1 lnx x->1+ (lnx)(x-1) 0
L' (1-x) 0
= lim -------------- [ --- type ]
x->1+ (xlnx)+(x-1) 0
L' -1
= lim ---------
x->1+ (lnx+2)
1
= - ---
2
: 3. 完全不知道怎麼算...
: Find the derivatives
: y = log (6x^ln2)
: 3
d(log x)
a 1
as ---------- = ----------
dx (x)(lna)
by chain rule
(ln2-1)
(ln2) x (ln2)
y' = ---------------- = ----------
ln2 (x)(ln3)
x ln3
--
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