在平面曲线中,曲率(curvature)是表示曲线在某一点的弯曲程度的数值,如图,圆
、
、
在点Q处的弯曲程度依次增大,而直线在点Q处的弯曲程度最小,曲率越大,表示曲线的弯曲程度越大.曲线的曲率定义如下:若
是
的导函数,
是
的导函数,则曲线
在点
处的曲率
,则余弦曲线
在
处的曲率为________ ;正弦曲线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/588bbf780d49cf4d29802c2e4126f112.png)
曲率K的平方
的最大值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aac282e92da3691942a6ba8511de2303.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](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/b61f2eb9e9804c3367344d4ede645420.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1242ec96ac54e2fd418988d5190a88.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6889205677dfb9a02934c36088b75d7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2581192317ef233ccdccfc48ac29b52b.png)
2023·河南·三模 查看更多[4]
河南省商丘市等2地2023届高三三模数学(理)试题河北省秦皇岛市青龙满族自治县青龙实验中学联考2023届高三冲刺卷(三)数学试题(已下线)第四套 复盘卷(已下线)专题8 函数新定义问题(过关集训)(压轴题大全)
更新时间:2023-07-27 14:41:22
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【推荐2】直线
与曲线
相切,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c4bad4325044ec1962f479ebd19165d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ca236f14a00672fe3e33fb603f9535.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
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名校
解题方法
【推荐1】已知实数
满足
,则
的值是__________ ,
的取值集合是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1845c3646482ae17a78dba94c01352f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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【推荐2】正割(Secant,sec)是三角函数的一种,正割的数学符号为sec,出自英文secant.该符号最早由数学家吉拉德在他的著作《三角学》中所用,正割与余弦互为倒数,即
.若函数
,则下列结论正确的有__
①函数
的图像关于直线
对称;
②函数
图像在
处的切线与
轴平行,且与
轴的距离为
;
③函数
在区间
上单调递增;
④
为奇函数,且
有最大值,无最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb197c2085236625d0a69b64bafbee9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc5e13686511bf1856bb5a088936748.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ff420ca0d6e2e7d434a933cf6c5792b.png)
②函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a90bc584ca10426b4418a275d62bfb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ebba6ed1add0fe647c0226614b9290.png)
③函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aba78fdda35eed1f2ac879398d88348b.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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【推荐3】若函数
存在两个极值点
和
,则
取值范围为____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98ecd30601ef10a6365e655f23b9af9d.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/4bfc8f775c0c874c4ea920136a91db8f.png)
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【推荐1】已知
是函数y=f(x)的导函数,定义
为
的导函数,若方程
=0有实数解x0,则称点(x0,f(x0))为函数y=f(x)的拐点,经研究发现,所有的三次函数f(x)=ax3+bx2+cx+d(a≠0)都有拐点,且都有对称中心,其拐点就是对称中心,设f(x)=x3﹣3x2﹣3x+6,则f(
)+f(
)+……+f(
)=_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1fd30c0905092ba072a910dcbb50e44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1fd30c0905092ba072a910dcbb50e44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d093b6a5199dab9d623b41d85d25677.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fbae15b4f8bd0d0bd16668739310eb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b81cc2f9fdb7d959945723c4dc7ddb5f.png)
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【推荐2】设函数
图象上不同两点
,
处的切线的斜率分别是
,
,规定
(
为线段
的长度)叫做曲线
在点
与点
之间的“弯曲度”,给出以下命题:
①函数
图象上两点
与
的横坐标分别为1和
,则
;
②存在这样的函数,图象上任意两点之间的“弯曲度”为常数;
③设点
,
是抛物线
上不同的两点,则
;
④设曲线
(
是自然对数的底数)上不同两点
,
,则
.
其中真命题的序号为__________ .(将所有真命题的序号都填上)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6ff82ebdfad5e7de1c7487b0b817a7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a53e311ee0b5085e7e5a45c606daa5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8605ae9897d5d6f0679b4aa80e014bda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17b3e87e9bb00d9ba09cb5660aebd76f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb7d70c30402ee0eeaab96cc6eefc0cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaff41080fdea43eea7efedf9ebc1498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c904567c3b3734e1eca8d042ef7a7b2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b9194547561993c2c98a4f32201012c.png)
②存在这样的函数,图象上任意两点之间的“弯曲度”为常数;
③设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b629bea8e22de9bfc49158e2289871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad613217bdff0b1c225e3e5ca31eec4c.png)
④设曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eae1b87c23b45ce5e5e74d5b1d73234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6ff82ebdfad5e7de1c7487b0b817a7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a53e311ee0b5085e7e5a45c606daa5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d456cce6e8beeff190657ed57e3e05.png)
其中真命题的序号为
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