設
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020717706932.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020717706486.png)
,Q=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020717721488.png)
;若將
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020717737508.png)
,lgQ,lgP適當排序后可構成公差為1的等差數(shù)列
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020717752456.png)
的前三項.
(1)試比較M、P、Q的大��;
(2)求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020717768283.png)
的值及
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020717752456.png)
的通項;
(3)記函數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240207178151271.png)
的圖象在
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020717830266.png)
軸上截得的線段長為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020717846365.png)
,
設
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240207178621107.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020717862523.png)
,求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020717877373.png)
,并證明
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020717893946.png)
.
(1)當
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020717924532.png)
時:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020717940621.png)
;當
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020717971396.png)
時:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020717986619.png)
;當
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020718033552.png)
時:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020718049622.png)
;
(2)當
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020717924532.png)
時:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020718080884.png)
;當
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020718033552.png)
時:無解.
試題分析:(1)兩兩之間作差比較大�。唬�2)根據(jù)第(1)問的結果結合等差數(shù)列項的關系求解;(3)先求出線段長
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020717846365.png)
,再表示出
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020718127458.png)
,通過裂項相消化簡求值
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020717877373.png)
,再結合放縮法求范圍
試題解析:(1)由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240207181581806.png)
得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020718189537.png)
2分
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240207181891364.png)
3分
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240207182051320.png)
4分
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020718220570.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020718236512.png)
又
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020718252235.png)
當
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020718189537.png)
時,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020718283717.png)
,
當
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020717924532.png)
時,即
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020718314435.png)
,則
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020717940621.png)
5分
當
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020717971396.png)
時,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020718376417.png)
,則
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020717986619.png)
當
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020718033552.png)
時,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020718423443.png)
,則
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020718049622.png)
(2)當
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020717924532.png)
時,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240207184701135.png)
即
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020718470939.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020718486195.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240207185171526.png)
解得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020718532453.png)
,從而
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240207185641008.png)
7分
當
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020718033552.png)
時,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240207185951107.png)
即
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020718595950.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020718486195.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240207186261439.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020717768283.png)
無解. 8分
(3)設
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020718657447.png)
與
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020717830266.png)
軸交點為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020718704684.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020718486195.png)
當
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020718657447.png)
=0時有
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020718735855.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240207187511004.png)
9分
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240207187661170.png)
又
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020718782794.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824020718813637.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240207188291134.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240207188441736.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240207189381885.png)
11分
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240207189541686.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240207189691918.png)
14分
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