名校
解题方法
1 . 已知函数
,则当自变量
从
变为
时,下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec6049f18dd88f7c4d4c9a1143058dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
A.函数值减少了6 | B.函数的平均变化率为2 |
C.函数在![]() ![]() | D.函数值先变大后变小 |
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名校
解题方法
2 . 已知函数
的两个极值点分别为2,3.
(1)求
,
的值,并求出函数
的极值;
(2)已知
,求证:不等式
在
上恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4257891e41280fe14712668856d0489.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047fa89ef19fb525f45f85e0c7509403.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aaada27ba11bcd779d26a63b1f91bb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
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3 . 对于定义域为
的函数
,若
,使得
,其中
,则称
为“可移
相反数函数”,
是函数
的“可移
相反数点”.已知
,
.
(1)若
是函数
的“可移2相反数点”,求
;
(2)若
,且
是函数
的“可移4相反数点”,求函数
的单调区间;
(3)设
若函数
在
上恰有2个“可移1相反数点”,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c42ef103bbb40a9c414ba273a16fa32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54739d72b5c319dcb4a6bc632256e813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c80c26a794a844127aae7dee87c93b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec6263576e5c3f2324a8dac311476bf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/670f35aac7f9bd8acf6fc5cd4e119b59.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d6c0bbfde440305a1de1e939ac78082.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f01ff53404ba146b39bd9e12dd68afbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544f91d4fb22c571db9f8481b72a0419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
解题方法
4 . 已知函数
的导函数
的图象如图所示,则下列说法错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090a91e4f3c8930674f98a9fa527709b.png)
A.函数![]() ![]() | B.函数![]() |
C.函数![]() ![]() | D.函数![]() ![]() |
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5 . 已知
是等比数列
的前
项和,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad9bd877ed7ca3fe1e3616815f4171a9.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.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/c16f31554d0bd97d85726972a28f21a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad9bd877ed7ca3fe1e3616815f4171a9.png)
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解题方法
6 . 已知数列
的前
项和为
,
,且数列
的前
项和为
.
(1)求数列
的通项公式;
(2)求证:
.
![](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/ed464bec8b75dd2d7f0c01552da113d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1272a6906aa7a79f4454d9fc4ff8df49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cadc27a59a738b9f6ae29fa7883754a3.png)
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7 . 已知函数
,
,若函数
与
的图象在
上恰有2个交点
,
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed3aec19f4ad1dac8a1710b888d2dd17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/391e64453fa47903c5b71260069670bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ad9a4881ebe1a4a566d0fab96d71baa.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
8 . 已知斐波那契数列:1,1,2,3,5,8,13,21,34,55,…的第
个数记为
,则
,
,已知
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c6530eb342f81833f40922711a3dbd.png)
______ .(用含
,
的代数式表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/157e55df96e0c1d1fd2663a469467b52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7885a0090b2cab1a7501209f691747c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3501d2c812358571d24ff7b4af0a2276.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dc977cdce5b10ab1fd62d33fa650edf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2658dfed798294e1c9f830349a9a4499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c6530eb342f81833f40922711a3dbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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9 . 要得到函数
的图象,只需将
的图象( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73fbe792889b097e27584b777064350a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb98c29354b0a57c88526044e1fcd303.png)
A.向右平移![]() |
B.向左平移![]() |
C.向左平移![]() |
D.向右平移![]() |
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解题方法
10 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f33062df5d816d6f8af194445c0189.png)
(1)若点
在角
的终边上,求
的值
(2)若
,求
的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f33062df5d816d6f8af194445c0189.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b20af7617b581d6b67d3d51709365681.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fbc7cada2f52172bde879638dbda0ff.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd65d7c5e979706d391163aee2c18cb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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