名校
解题方法
1 . 已知离散型随机变量
的分布列为
若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
X | 0 | 1 |
P |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39d9a8dc1d0be0b09e45bf8eb296a272.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f412feb8dcad5599ddfe1d1ceb00ac0b.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
解题方法
2 . 已知数列
的前
项和为
,且
.
(1)求
的通项公式;
(2)证明:数列
为等差数列.
![](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/5635fbe6fabbf7eb4ab1670c06fba091.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8194a62bc60a9da9b5cf76f9dc0fa09.png)
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解题方法
3 . 已知数列
满足
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c3082aa4390cb5575e6030d521e3e37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53271336649378a043f9da8b8bdc1cfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42e4487468ab2823d6dbf7f0ebd2eb38.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 已知函数
.
(1)求函数
的图象在点
处的切线方程;
(2)求函数
在区间
上的最大值与最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eedaa6aad781cb80241b78ae9d4c97cc.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9770b18d9984172e6c08bf0921ec4200.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17b63fb475fbdacbbb8eb2bf6a6716d2.png)
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5 . 已知直线
是曲线
的切线,则切点坐标为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ece4a9d93801d9f28cf3cd91ccba5e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12be206d66e65eb92ef08bad8cd8f71d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
6 . 已知椭圆
的左、右焦点分别为
,
,离心率为
,过椭圆的左焦点
作不与x轴重合的直线MN与椭圆相交于M,N两点,
的周长为8,过点M作直线
的垂线ME,E为垂足.
(1)求椭圆C的标准方程;
(2)证明:直线EN经过定点P,并求定点P的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5585a42c8f07ad90b94ace9db3d78994.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae65a3b431bc5e09408beb3466908d6a.png)
(1)求椭圆C的标准方程;
(2)证明:直线EN经过定点P,并求定点P的坐标.
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7 . 在等差数列
中,
,
.
(1)求数列
的首项
和公差
;
(2)设数列
的前n项和为
,求
的最小值及取最小值时n的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff52aa657973485243c460aad1502267.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00d6bd814515a297f39e59b3ffa2cffa.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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8 . 已知数列
是公差为
的等差数列,数列
是公比为
的等比数列,且
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
,
.
(1)求数列
和
的通项公式;
(2)求数列
的前
项和
的最值;
(3)设
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af4cd53fb75a76ee4d470730543716a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/386ecd54032e020fe79555311d12151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31b84ac5df922d8bcc39c60c362073a0.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1948084deb16af8ae5bd7aae0fbc58a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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解题方法
9 . 已知函数
,
,若对于任意的![](https://staticzujuan.xkw.com/quesimg/Upload/formula/244af58c69c119a21c512a8ea77e4dac.png)
,使得
恒成立,则实数
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d286f10c2662c15a7e6b45394d20f56c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/262077581baf603acf7be972c8afb42e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/244af58c69c119a21c512a8ea77e4dac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/032e8dc00cdc96860c9cbf8ac09677fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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10 . 已知函数
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1044dcf4fba551e1b7fbfeb895ea08c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfc45f485fd69c910ff1b777fc87bf47.png)
A.1 | B.![]() | C.![]() | D.![]() |
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