名校
解题方法
1 . 如图是一个球形围墙灯,该灯的底座可以近似看作正四棱台.球形灯与底座刚好相切,切点为正四棱台上底面中心,且球形灯内切于底座四棱台的外接球.若正四棱台的上底面边长为4,下底面边长为2,侧棱长为
,则球形灯半径
与正四棱台外接球半径
的比值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://img.xkw.com/dksih/QBM/2024/2/24/3439881745645568/3442029472153600/STEM/0066b9762966488a85b34c65df195b17.png?resizew=105)
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2 . 已知函数
.
(1)若
,且
图象关于
对称,求实数
的值;
(2)若
,
(i)方程
恰有一个实根,求实数
的取值范围;
(ii)设
,若对任意
,当
时,满足
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb49512c66fdf46280daa506f5458004.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9be033199f77a8822a8514eafab5162d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86f59eb2942c435d69c1e48c2c61c111.png)
(i)方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e735656890d668f67f1538fe702b366a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(ii)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fc373640d8d66865998853b3c3f7be5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71530343bd5d7121c2e77b10aff7bd50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a57318f5659bc916624d975b7146e8a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
3 . 已知函数
,
.
(1)若函数
,
,求
的最值;
(2)设函数
,
在区间
上连续不断,证明:函数
有且只有一个零点
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7edecfbf1b4e1052468d209e8f017a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dce2bfe6e1fde9265d2a07c42bbdf58.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31bfb22bf37b71482bd4649852a7dacc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0eac2b31a19918895e5af2d316490e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cc17049fc86f1ef6b73f8a14fc24d41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f77f8111c7805e673a644b0a690dcc.png)
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解题方法
4 . 已知函数
在区间
上的最大值为3.
(1)求
的值;
(2)当
时,
,对于给定的实数
,若方程
有解,则记该方程所有解的和为
,求
的所有可能取值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55d35287ce34b6c83e7c9724f86820c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d51992c05a557cf6058664f1f8961e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0a68eadbcb9953c6d7fc17ef2763ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4fa6973b952c0ca9e0268e2e40194ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72c77a9531c3fd1d25b927cc29b0ad59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2217dfd3de10c834acb8aea9ec9e3a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2217dfd3de10c834acb8aea9ec9e3a5a.png)
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名校
解题方法
5 . 函数
的图象关于坐标原点成中心对称的充要条件是函数
为奇函数,可以将其推广为:函数
的图象关于点
成中心对称的充要条件是函数
为
关于
的奇函数,给定函数
,关于
中心对称.
(1)求
的值![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ca6fa9955690cec01db601e3abce0c.png)
(2)已知函数
,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/1c7028a5fa4d781d382ca3b73b74796e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c7028a5fa4d781d382ca3b73b74796e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c7028a5fa4d781d382ca3b73b74796e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291aaad429837ab6dc1f99b9f7327cf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98f4cf449b51f221f9cb26e71a9dbebb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a42e14c5d826813dd33e04be2d2c26d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1f5fc756bf1aa3099dba53a6caba5a8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ca6fa9955690cec01db601e3abce0c.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae9dccd1d5763d4c2a8799ead64f475d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ee1e47231d0c468d7e2d720a0fdeee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1247c1725b0a2037e53cbf5f7a668483.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9af9f0245165190c43c12ab642a97a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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名校
解题方法
6 . 设函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc8f3fb58748fc489ef16b5ed4d45808.png)
(1)当
时,判断
的奇偶性,并说明理由;
(2)当
时,若对任意的
,均有
成立,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f28b48f9ee7f155ca60e022e8c78d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc8f3fb58748fc489ef16b5ed4d45808.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d3c880f30beda2ebf604976dc159c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09fcc7732fd7eac9a392b5e4cab0331.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a180d480ee4f68609f4bf7d068e4316.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51442bf0ef97e173588b54ee77db26b5.png)
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名校
解题方法
7 . 若
时,不等式
恒成立,则实数
可取下面哪些值( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f60974b156ccb19c9430e0671dd954c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/135dd2b22a6de8ee644adc100d5d1e67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a88a1d706f453ebe641928d539a55a7b.png)
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a88a1d706f453ebe641928d539a55a7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d75d042a2fd6581382fef773402bd78.png)
A.![]() ![]() |
B.若![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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名校
解题方法
9 . 已知函数
在
上为奇函数,
.
(1)求实数m的值;
(2)存在
,使
成立.
(i)求t的取值范围;
(ii)若
恒成立,求n的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23db0aced2530841600107296baa0df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
(1)求实数m的值;
(2)存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc73297caf4c1813530134dc85080cdb.png)
(i)求t的取值范围;
(ii)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0da4a67544afb4c0edc031607e10cd91.png)
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名校
解题方法
10 . 已知函数
,
,
,
,
与
的图象共有
个不同的交点
、
、
、
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed398adf2e23a4b691c4477070416925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a6e5e0b0c6d24e08772d6799ebb0167.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fc878ea92f396d8559210f4bd086b0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a6e5e0b0c6d24e08772d6799ebb0167.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56720e2f2b0ddd72156da495923698da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2852ae85cfcc804b3192ea8543c88938.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92abae836b8026511113ad8c3ea23028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfe80f4988dab6cba196af6d9557f398.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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