已知函數(shù)
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.
(1)試判斷
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在
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上的單調(diào)性;
(2)當
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時,求證:函數(shù)
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的值域的長度大于
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(閉區(qū)間[
m,
n]的長度定義為
n-
m).
(1)函數(shù)
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在
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上為增函數(shù).(2)同解析。
(1)∵
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,
∴
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,
∴
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時
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,
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時
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;
∴函數(shù)
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在
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上為增函數(shù).
(2)由(1)知
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;
即
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, ∴
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(﹡)
令
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, ∵
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, ∴
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,
∴由(﹡)式得
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,即為
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;
∵函數(shù)
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的值域為
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,
∴函數(shù)
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的值域的長度為
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,
∴函數(shù)
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的值域的長度大于
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
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
有且僅有兩個不動點0和2.
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)=1,
求證:

<

<
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bn}的前
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
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;②對
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,其中
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為實數(shù),且
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在
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處取得的極值為
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。
⑴求
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