1 . 在数学中用符号“
”表示“连乘”,类似于
表示“连加”,例如:
,已知函数
,记
为
的导函数,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6706fe00b4e231e62d9ecbec567d526b.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efd4ec09a6ea86e7eac893151a14b357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56901beac7124c75c6a6e0e5dfb08950.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/939c3b2122428f8032b1b4f5ced38e3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74b41bb3c8d792be7e230f04c962fdfc.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72e1af9ffcb9091308c33a0f78af24b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6706fe00b4e231e62d9ecbec567d526b.png)
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2 . 若
是区间
上的单调函数,满足
,
,且
(
为函数
的导数),则可用牛顿切线法求
在区间
上的根
的近似值:取初始值
,依次求出
图象在点
处的切线与x轴交点的横坐标
,当
与
的误差估计值
(m为
的最小值)在要求范围内时,可将相应的
作为
的近似值.用上述方法求方程
在区间
上的根的近似值时,若误差估计值不超过0.01,则满足条件的k的最小值为______ ,相应的
值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df0dd6144e9a30d1a063b690033c3f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10acd6d864583617dd3e71240bf0c857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/596afe6f8149e39c53d36a759bee6151.png)
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3 . 用充气筒吹气球,气球会鼓起来,假设此时气球是一个标准的球体,且气球的体积
随着气球半径r的增大而增大.当半径
时,气球的体积
相对于r的瞬时变化率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2849deb96094a8bd4ee643d1da75b58c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7551011cfb75b26f35b07d6617c6a18b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af0f92ea65504a3ac0de9ef30ee3a9d3.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 已知
(
,且
),若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5918d80153996c830e52e46113c4771.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e77efa572264036426c64052666b7acd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0baedc4d7e690ab3f7d80d30ba0a9efe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/152443f5b6290aeea3d50342f9b35b35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 曲线的曲率就是针对曲线上某个点的切线方向角对弧长的转动率,表明曲线偏离直线的程度,曲率越大,表示曲线的弯曲程度越大,工程规划中常需要计算曲率,如高铁的弯道设计.曲线
在点
曲率的计算公式是
,其中
是
的导函数.则曲线
上点的曲率的最大值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07fa72fc4959804b944bfaa93dbe2b21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f3397b19388a115af9cbffec9fb209c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c30fff3db26d531f34b704ca244f0d42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a550ccbc8921121c14419899f4538ff6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/377a2333ff8c63cbdb20b882d6d5a7ec.png)
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湖南省长沙市雅礼教育集团2022-2023学年高二上学期期末数学试题上海市复旦大学附属中学2022-2023学年高二下学期3月月考数学试题(已下线)第五篇 向量与几何 专题21 曲率与曲率圆 微点3 曲率与曲率圆综合训练(已下线)第五篇 向量与几何 专题21 曲率与曲率圆 微点2 曲率与曲率圆(二)上海市川沙中学2023-2024学年高二下学期期中考试数学试题
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6 . 下列说法中正确的有( )
A.![]() |
B.已知函数![]() ![]() ![]() ![]() |
C.一质点的运动方程为![]() ![]() |
D.已知函数![]() ![]() |
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