1 . 定义在
上的函数
有
,则
的单调增区间是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dcd18de56ce1be490472261062a9741.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
2 . 已知函数
(
且
),若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5918d80153996c830e52e46113c4771.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eb2db2cf720ecda0ef57128f7f59e0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0baedc4d7e690ab3f7d80d30ba0a9efe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b55f8fccade0d2612bf7575f638b985.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
A.2 | B.![]() | C.3 | D.![]() |
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解题方法
3 . 函数
的极大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43f170602cfec4eb40f9a3d6ca6cdf63.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 一辆汽车在公路上沿直线变速行驶,假设
时汽车的速度(单位:
)为
,则汽车在第
时的瞬时加速度为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c1a48b92c61d209d0556e4cd8fdb70b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53afeaf21f93091b71608d21540be239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f44e533016c8d684e6c692c14afe803.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4c1f9c14db1a10006f079739ffa690d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 下列导数公式正确的选项序号是_________ .
①
(其中
且
);
②
;
③
(其中
且
);
④
(其中
且
)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/269c90a702e49c4d2b3262a7348b531e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ae87a22e512ae0367940d303beb4f8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4313f830e9be762a14205f2c2141d7.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3785a32c15c4ed1944e597a53d8069e6.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4732fe13220ab20a82f96d65aabc4fb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ffa20008862caa75ac0461ca7b9c01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
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6 . 事实上,对于两个函数
和
的商的导数,我们有如下法则:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bae54ea79b90e1710336975ad63f55cd.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5085887422e1722dd9bdfd14c7fc8ef9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bae54ea79b90e1710336975ad63f55cd.png)
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7 . 一般地,函数
的单调性与导函数
的正负之间具有如下的关系:在某个区间
上,如果_________ ,那么函数
在区间
上单调递增;在某个区间
上,如果_________ ,那么函数
在区间
上单调递减.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
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8 . 函数
在
处的导数
就是函数
的图象在点
处的切线的_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91421e7703d87617f50270178decd18a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25be20e3724274132cb83b16deaeecfc.png)
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解题方法
9 . 已知
分别为椭圆
的左顶点和左焦点,直线
与椭圆交于
两点,若直线
交线段
于
,则椭圆的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8348c89c6f13053325f4e1c62e29a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0b9af8dcc33088cedc3fbefaab69970.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
10 . 等比数列
的前
项和为
,且数列
的公比为32,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e030e6477f83384109416cbde2479bf7.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/051392edad70a34634b89bdac068f67f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e030e6477f83384109416cbde2479bf7.png)
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