Re: [微分] 課本習題

[Honor1984 (希望願望成真)]

※ 引述《victor7935 (victor)》之銘言：
: 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

你的教授可能是鄉民

你最好小心一點  哈哈

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推 victor7935:好可怕....
推 lovehan:教授會來初微板幫鄉民解題嗎？ 0_0a
推 victor7935:不知道...數學版可能會喔!!
→ victor7935:教授說不定覺得眼熟這些題目..然後..po
→ victor7935:出有問題的答案= = ''
→ victor7935:再把我揪出來....好恐怖!!