1 . 已知恰有两个零点,求
的取值范围.
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2 . 已知,求
的可能取值.
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3 . 将所有平面向量组成的集合记作
,
是从
到
的映射,记作
或
,其中
,
,
,
,
,
,都是实数.定义映射
的模为:在
的条件下
的最大值,记作
.若存在非零向量
,及实数
使得
,则称
为
的一个特征值.
(1)若
,求
;
(2)如果
,计算
的特征值,并求相应的
;
(3)若
,要使
有唯一的特征值,实数
,
,
,
应满足什么条件?试找出一个映射
,满足以下两个条件:①有唯一的特征值
;②
,并验证
满足这两个条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c85067c53e936ef32da818efe04bdbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c85067c53e936ef32da818efe04bdbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c85067c53e936ef32da818efe04bdbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02de2ea205a54acd8cd7e279b96d1c5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39549972b3c02bd84637471fb171ae90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0b2929e18e7737669e001ec83b4543.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f921a664a3f2a8696f7702bb38ad61f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da1a9fb3904514272b50fa3339ee2b40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e9c5e3816909bd49a229130af166698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edbc4c88fe1a586aef39e92e925f0337.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ad9a98e9aae2623ea32b1b05960470.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6938ce64829c28318021579c6e45b4a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a072f92e9330b67545633ef422c3ee2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edbc4c88fe1a586aef39e92e925f0337.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72819d3bcd97399a6ed89f87efaa92b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/552355ddba8eef1ca3bf15eb53d79622.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2322e48ae3b2a166f061eb4aaf39f355.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a668834bb908d31cb0fac925c1c9dd04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
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2022-03-04更新
|
779次组卷
|
4卷引用:北京师范大学附属实验中学2022届高三下学期摸底考试数学试题
4 . 设实函数
满足
,问是否存在整数n,使
也为整数?若存在,求出所有的n;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad4608d76039a3b61ec7502c5e645e22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d4fc8faefb26b233d4aa9dbef043aae.png)
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5 . 函数
是定义在
上,在
中取值的严格增函数(如果任意的
,当
时,有
,则称
是
上的严格增函数),并且满足条件
.试求
之值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa7a84d7e5d6236009a8be655bd500fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcc342b78b8c829d22ef5325354abed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e2f24b4fa5308650a244d954f78f09b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4960de7a0fee1427e1b047fc796770a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fed8602adcaac7b9ae827297407a3b1.png)
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6 . 设
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b16043729e7fb6c3129b8739c7bc7dca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54ebda5018a8227c05b0fe0cab555c45.png)
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7 . 若
有两个不同的实数解
.求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1da5ff5a31a22cd85bf5dbf472fe3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acb3f0ed152b8bdd053959d3479d63b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2ff89c22de06c89dc0ff933e02631ee.png)
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8 . 设x是实数,且
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1897306176ade0dd5e3ea0ddeb9d085a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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9 . 已知
是定义在实数集上的函数,且
.
(1)试证:
是周期函数.
(2)若
,试求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e31cfd8c2f3b621c1a00e2f4627fba53.png)
(1)试证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72f37d3cf60e305998683f6735b4d3b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94f24255c3a5f9418bed4eaef65a7235.png)
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10 . 已知
为定义在实数集
上的函数,对任意的
、
,恒有
.求
,并计算
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54dad48527a47eab4a5916ab0421cc71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9423225dee4717741ceba039198dd6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba50b0de429edbfc86a9d72ba968bf91.png)
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