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# 微積分考古題(王子請幫幫忙)

<1>Let f:[a,b][a,b] be a continuously differentiable function. suppose that

max 1f'(x)1<1

a<x<b

prove that there exists a unique solution f(x)-x=0

(Hint:Intermediate Value Theorem and Mean Value Theorem)

第二行那是絕對直

<2>find the Maclaurin series of √(1+x) and the radius of convergence

### 1 Answer

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- densityLv 61 decade agoFavorite Answer
第一題的出處在哪?我想看原始題目!

等我看完再一併作答!

2008-01-29 02:45:06 補充：

1.首先用中間值定理證明他至少有ㄧ解再用均值定理證明此解為唯一. 這個題目是一維的固定點定理!!2.利用規律求解!

參考詳解請如下,請參閱!!

Source(s): myself

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