1 . 已知函数
,
,其中a为整数且
.记
为
的极值点,若
存在两个不同的零点
,
,
(1)求a的最小值;
(2)求证:
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b9f3156ad64e96aea8cdf9eb9397791.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67419d367491963b4b091e3fd0704c64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ede78fd7ac619ea597856254bb5d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c4588a79e160bca3711b1151a52f26b.png)
(1)求a的最小值;
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a98291a95a597a74bfce7c95546f023.png)
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2 . 已知函数
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f21a50eec669449f41225526fce3d7f.png)
A.![]() ![]() | B.函数![]() |
C.函数![]() ![]() | D.![]() |
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3 . 已知函数
,若关于
的方程
在
上恰有一个实数根
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90c7ba821bffc75af7c94766bcd1d4e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53766c5b2394eb642ecf4eacb8edb765.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b42bb31208a4142c489609ef05c2922b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b51021360a665f914d38085cfd91e88.png)
A.![]() | B.![]() | C.![]() | D.2 |
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4卷引用:高三数学考前押题卷3
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解题方法
4 . 将函数
的零点按照从小到大的顺序排列,得到数列
,且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b368c47922b40534ed2c75177466ba56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/352d9b76dcf639368fa68cae70149802.png)
A.![]() | B.![]() ![]() |
C.![]() | D.![]() ![]() ![]() |
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5 . 已知函数
其中
,且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4911900ac1c8fb5b0bc6b64f1ad6f030.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166cc3bc78f3870fc454556a1c8b5dd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b73abfe4bc26b1ded680d7abb1a2cac.png)
A.![]() | B.函数![]() |
C.![]() | D.![]() |
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6 . 已知函数
,则关于
方程
的根个数不可能是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8dc99a83165850cfdb3865907ca7949.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edfde98d1334bbb9375d8df7130e379c.png)
A.0个 | B.1个 | C.2个 | D.3个 |
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7 . 已知函数
,则下列说法中正确的个数是( )
①当
时,函数
有且只有一个零点;
②当
时,函数
为奇函数,则正数
的最小值为
;
③若函数
在
上单调递增,则
的最小值为
;
④若函数
在
上恰有两个极值点,则
的取值范围为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7de2557c94581de871a526d2a98b78d6.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c05a467ddaa138590b3b56615c2c42a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d08c98071305120f7035bdff622deae.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c05a467ddaa138590b3b56615c2c42a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40a46a0fc7c90b66b3aeb64aa64448eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
③若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fed440b9f974492068a68203e5029f98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
④若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71163f419555f2ed76075c8ff659fbfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67b0d17ea32654ec2b7946078158cfc8.png)
A.1 | B.2 | C.3 | D.4 |
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8 . 若
,
,
,则正数
大小关系是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbd09e560887f8b826206e5dcbfe0d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95f3406589c80c548c2072a89357589a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615490e1ec51137c8792f0418db24b9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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9 . 在平面直角坐标系
中,如图放置的边长为2的正方形
沿
轴滚动(无滑动滚动),点
恰好经过坐标原点,设顶点
的轨迹方程是
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f22fa66bd977256019ab7c42f66ac75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
A.方程![]() ![]() |
B.![]() |
C.![]() ![]() |
D.对任意![]() ![]() |
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解题方法
10 . 已知函数 ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4736a092ca2f06fcf287d12184fcd28a.png)
方程
有两个不同的根,分别是
则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4736a092ca2f06fcf287d12184fcd28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac86c2a5c90972102259bc2e7ca4576.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b90997b3b12fb9fe293bc7d45a6e015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c58cc80f792a9262c4da33fabd21e95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97dad16e4910ec15add074c4077b0e86.png)
A.![]() | B.3 | C.6 | D.9 |
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