已知二次函数
.
(1)令
,若函数
的图象与
轴无交点,求实数
的取值范围;
(2)设函数
,若对任意的
,总存在
,使得
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dceed2e7a0a44f06934d0262b6bbfac1.png)
(1)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83ef9f9f0a79e61a30f7da782cbb2fab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/462687ad505073ca98b88acb9ce2af8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0496d81c441e6cfa9c26ff7e83746eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/673eaea5bb52b5ec93a21de0db36c5cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe53bb5e833f83c2d8290d195fabf02b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
23-24高一上·吉林长春·期中 查看更多[3]
吉林省长春市东北师范大学附属中学2023-2024学年高一上学期10月期中数学试题广西南宁市广西大学附属中学2023-2024学年高一上学期期中段考数学试题(已下线)8.1 二分法与求方程近似解(十二大题型)(1)-【帮课堂】(苏教版2019必修第一册)
更新时间:2023-10-28 20:15:28
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【推荐1】已知集合
,
.
(1)若
,求实数
的取值范围;
(2)若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97af6fad038b3ff3fccdb4b47fd7967f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1446ee4288f5d3e66253f1b84b1c7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf22d7d1a965bda25168a233fb6290c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea9a4259cca10c1f5af28e621ebafd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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【推荐2】已知命题:“
,使得不等式
成立”是真命题.
(1)求实数m的取值集合A;
(2)设不等式
的解集为B,若
是
的充分条件,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be410fd42b9b3f5213afd76778c1871f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/888d01322e737b87dc2fc9581ebc51ad.png)
(1)求实数m的取值集合A;
(2)设不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47a0157717a03fbb146326749cd34477.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23af61cd402b3789af2401bde9cbefe.png)
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解题方法
【推荐1】已知函数
是定义在
上的奇函数,当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd6fdf6a9d3e460151465372beab090.png)
(1)求
的解析式;
(2)令函数
(
),若
,当
时,总有
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd6fdf6a9d3e460151465372beab090.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)令函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c74f6363d928d201b609514f3d6b2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ee681a20ee283caf90ef021cade610c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/968f04c26c183c66c7350061a3eebc59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
【推荐2】已知函数
是定义在
上的奇函数,且
.
(1)求实数
,
的值;
(2)判断函数
的单调性(不用证明),并解不等式
;
(3)若
对
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c7d5cc15feb11e75af69ab244e2e7e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/249a976e88133f3b3733f09137cf5c42.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/052844a1c37b4678b53634afc1f6da4c.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ab096a1a4d9506bb1a192ea902b1582.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a97047f1d2dbb951673fe843db27edf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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【推荐3】已知
是偶函数.
(1)求实数
的值;
(2)用定义法证明函数
在
上的单调性;
(3)解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdd6fdfcf1423355e36cc32eceaeccc4.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)用定义法证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe86cace140f2c3588ab115837bbfc9e.png)
(3)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28ef2a42778b3434ecd60d6e1eb07636.png)
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【推荐1】如图1,
,
是某地一个湖泊的两条互相垂直的湖堤,线段
和曲线段
分别是湖泊中的一座栈桥和一条防波堤.为观光旅游的需要,拟过栈桥
上某点
分别修建与
,
平行的栈桥
、
,且以
、
为边建一个跨越水面的三角形观光平台
.建立如图2所示的直角坐标系,测得线段
的方程是
,曲线段
的方程是
,设点
的坐标为
,记
.(题中所涉及的长度单位均为米,栈桥和防波堤都不计宽度)
![](https://img.xkw.com/dksih/QBM/2013/5/31/1571236368277504/1571236373594112/STEM/a3ce3dc63fe543a18bdb862fd3dda7c3.png)
(1)求
的取值范围;
(2)试写出三角形观光平台
面积
关于
的函数解析式,并求出该面积的最小值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67c015d99f2677951bdcd0447240ef93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30f954a8da05cc9144d4bf86f88e236a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67c015d99f2677951bdcd0447240ef93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30f954a8da05cc9144d4bf86f88e236a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede379e2df13ae6ad7e7cb4e883a273f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d45e100b7c57fa8365b64ff679c9a50b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f754fffa98deb2508acdeb8fa81eb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f50e0383945857f1531ce8ca6453fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2709f2a1698a145b12e19aa6bfdd810a.png)
![](https://img.xkw.com/dksih/QBM/2013/5/31/1571236368277504/1571236373594112/STEM/a3ce3dc63fe543a18bdb862fd3dda7c3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
(2)试写出三角形观光平台
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede379e2df13ae6ad7e7cb4e883a273f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb42ea4a7e095f585e6e4c63e1095026.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
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【推荐2】某乡镇响应“绿水青山就是金山银山”的号召,因地制宜地将该镇打造成“生态水果特色小镇”.经调研发现:某水果树的单株产量
(单位:千克)与施用肥料
(单位:千克)满足如下关系:
,肥料成本投入为
元,其他成本投入(如培育管理、施肥等人工费)
元.已知这种水果的市场售价大约15元/千克,且销售畅通供不应求,记该水果单株利润为
(单位:元).
(1)求单株利润
关于施用肥料
的关系式;
(2)当施用肥料的成本投入为多少元时,该水果单株利润最大?最大利润是多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d8fafd6f3f80d7dcfb838ed13109c6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b395a824c8962e50ea8dd950d83970f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e23b020e028ba9aee9547e77eaca05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)求单株利润
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)当施用肥料的成本投入为多少元时,该水果单株利润最大?最大利润是多少?
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【推荐1】已知定义域为
的单调函数
满足:
对任意
均成立.
(1)求
的值;若
,求
的值;
(2)若关于
的方程
有且仅有一个根,求实数
的取值集合.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af82699f1b2cf7875bf0671815ea64b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/617602d23a342cc2c6d367f0eecc9547.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74156327e5659301f391814605688899.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb04d514baf56eec084671b88898770b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72d5f425ddcd66f768c9a510601ca268.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aff0379c32196bcbe7d387b10ac629f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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解题方法
【推荐2】已知函数
,其中a∈R,且a≠0
(1)设h(x)=(2x-3)f (x),若函数y=h(x)图象与x轴恰有两个不同的交点,试求a的取值集合;
(2)求函数
在[0,1]上最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80923212fb2e77439887f6bbc204d177.png)
(1)设h(x)=(2x-3)f (x),若函数y=h(x)图象与x轴恰有两个不同的交点,试求a的取值集合;
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d300a3a6d3270bccac16b34fd7a3cb5b.png)
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【推荐3】已知函数
的部分图象如图所示.
的解析式及其单调递增区间;
(2)将函数
的图象上所有的点向右平移
个单位,再将所得图象上每一个点的横坐标变为原来的2倍(纵坐标不变),得到函数
的图象.若方程
在
上有三个不相等的实数根
,
求①求m的取值范围.
②求
的值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fb2b2fdc4e57e2d2de7115758518622.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)将函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aeb076bad84890e24dbdc945ad543cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91a09da1efd0f599dd4682f2284822b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a604fadcbf8568cbd8dacddd68443e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50f2c9ba604e34100159eb10cccd2b04.png)
求①求m的取值范围.
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26a8516b1db6979a28b07fd841c7f06b.png)
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