1 . 拓扑结构图在计算机通信、计算机网络结构设计和网络维护等方面有着重要的作用.某树形拓扑结构图如图所示,圆圈代表节点,每一个节点都有两个子节点,则到第10层一共有______ 个节点.(填写具体数字)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/30/553f2881-4150-4f3a-b8b8-5d61f2d4f337.png?resizew=150)
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2 . 过点
作曲线
的切线,请写出切线的方程______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6603d0aa20d5855490c5d16e8634477.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/938ff61757a67f266a910219fa0dd995.png)
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3 . 已知函数
,则
的最大值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/886631c1a36acb5d29a0683cebcd723b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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解题方法
4 . 已知双曲线
的左、右焦点分别为
,
,点
在
的左支上,过点
作
的一条渐近线的垂线,垂足为
,则当
取最小值16时,
面积的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef66f4832adc43902055a7e6d258037.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a31b19762dee424b24a25685e3012006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bad3be8e3fdeda3a12251d3751715e1.png)
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5 . 已知函数
,
,且
,都有
,若函数
在
上有且只有一个零点,则
的最大值为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db77de4df5ce7e8ff4be6ddb4f998918.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83703d33e8e04872aa316347b2133bfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3033291263ef14fbb35ae296117337b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec270afb8bfe12737ef8a8f7dd4bf1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
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6 . 牛顿曾经提出了在常温环境下的温度冷却模型
(t为时间,单位:分钟,
为环境温度,
为物体初始温度,
为冷却后温度),假设一杯开水温度
,环境温度
,常数
,大约经过________ 分钟水温降为30℃(参考数据:
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6861ea66b004cf4b9058032e2d3df15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4438bae1705c0f26beddf41322c087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f64fa38725c136504f723019a18dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf00b2b38708ff34059b6970e9f38a41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2fc0f9104ff36aab0aa266390af0ff0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d81febf743fd2ea37bb596890773f700.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f12a76edbb3e98e3ff41c03401769d1c.png)
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7 . 已知点F为抛物线
的焦点,
为抛物线上一点,且
,则该抛物线的准线方程为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf54a163cef69c4650f6dd0894f575ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83b173a5c1a243794a788b2a041da4a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1584d07b1e2ddc64349f0f5940f3a3e.png)
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8 . 已知
,若
有四个不同的零点,则t的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbad69de967d3873f571c72e4e4e49fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e89c2e159c04dee55d4b8ef18809fb45.png)
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2023-12-28更新
|
938次组卷
|
3卷引用:贵州省铜仁市石阡县民族中学等校2024届“3+3+3”高考备考诊断性联考(一)数学试题
贵州省铜仁市石阡县民族中学等校2024届“3+3+3”高考备考诊断性联考(一)数学试题江苏省苏州市南航苏州附中2024届高三上学期零模模拟数学试题(已下线)微考点2-1 新高考新试卷结构中导数中零点根的个数问题(2大题型)
解题方法
9 . 已知向量
,
,
满足
,
,
,则
的最大值是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d366d8fbb7258ee051f49977441e14a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0150d9c357f2f8f8deecacd3ef0545cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f93ac20aa3f83b16dc7e9444beda19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76d1209bee09e893f143d8982b2dc9d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84ade434cfd990949f8ae1f39da78e3c.png)
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10 .
的展开式中,
的系数为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/949ee9145321cd9b9e70c4eac4aba844.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02d8026e7e56b5a88c2bb9347c9d204d.png)
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