作者Honor1984 (希望愿望成真)
看板trans_math
标题Re: [微分] 课本习题
时间Sat Oct 25 17:08:44 2008
※ 引述《victor7935 (victor)》之铭言：
: 1.
: A function L has the property that L'(x) = 1/x for x≠0.
: Determine the derivative with respect to x of L(X^2 + 1).
u = x^2 +1
d/dx[L(u)] = L'(u) du/dx = 2x/(x^2+1)
: 2.The number a is called a double zero (or a zero of multiplicity 2)
: of the polynomial P if
: P(x) = (x-a)^2 q(x) and q(a)≠0.
: Prove that if a is a double zero of P,then a is a zero of both P and P',
: and p"(a)≠0.
P(x) = (x-a)^2 q(x) and q(a)≠0
=> P(a) = 0
P'(x) = 2(x-a)q(x) + (x-a)^2 q'(x)
=> P'(a) = 0
P''(x) = 2q(x) + 2(x-a)q'(x) + 2(x-a)q'(x) + (x-a)^2q''(x)
=> P''(a) = 2q(a) =/= 0
你的教授可能是乡民
你最好小心一点 哈哈
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◆ From: 122.124.101.60
1F：推 victor7935:好可怕....140.123.221.147 10/25 17:12
2F：推 lovehan:教授会来初微板帮乡民解题吗？ 0_0a 220.135.74.200 10/25 18:51
3F：推 victor7935:不知道...数学版可能会喔!!140.123.221.147 10/25 19:24
4F：→ victor7935:教授说不定觉得眼熟这些题目..然後..po140.123.221.147 10/25 19:24
5F：→ victor7935:出有问题的答案= = ''140.123.221.147 10/25 19:25
6F：→ victor7935:再把我揪出来....好恐怖!!140.123.221.147 10/25 19:25