解题方法
1 . 已知函数
.
(1)讨论函数
的单调性;
(2)若
,求证:当
时,
;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb140d3c2c4f67ac39de4b9592e04897.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6174a7497c19a22a2a506bfd568415f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790daaa89fc9d093f45023becf765697.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d349bc82a16ecc6e075b36c3376c853.png)
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解题方法
2 . 已知函数
.
(1)证明:
;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450b0d900f37939ed77fc8635908f18a.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8661079c5f29d5db641eefed0fe6cd51.png)
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解题方法
3 . 已知函数
.
(1)证明:
;
(2)证明:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450b0d900f37939ed77fc8635908f18a.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bfe21d5e79f8c8494e3f4dbe7391fe3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e31d5f5293de76ffd02c8125caa9eb6.png)
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解题方法
4 . 某圆锥的母线长为10cm,当其体积最大时,圆锥的高为________ cm.
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5 . 设函数
.(其中
为自然对数的底数)
(1)若
,求
在
处的切线方程;
(2)证明:
,当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89e93488a1739a33a923e1ae748375bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11204e2fb6e560bf7a4ca26eaebfc526.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5cf36bbcd71d1b792005f1e3055dff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81a51f385717d150efe64f61926c8b7f.png)
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解题方法
6 . 设函数
.(其中
为自然对数的底数)
(1)若
在区间
内单调递增,求a的取值范围;
(2)证明:
,当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74163a59d5f045ab9d02fa298b0c1d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11204e2fb6e560bf7a4ca26eaebfc526.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5cf36bbcd71d1b792005f1e3055dff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e155711ec8cef387f1bb648bf0dbc56.png)
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解题方法
7 . 已知函数
.
(1)若
在点
处的切线方程为
,求实数
的值;
(2)设
.在(1)的条件下,若满足
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81e87974df3be6d882465d500b294b3e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9f8845aa2b51c460f2d798c9f62fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9355031ea0b2dc9cef3777621bc6d38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bca76addc638efe4e09e55bc8cd6f38d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/653fc3cce9f12abbff235bb5576041b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2df1dd2aca2f976cec14e60cf8d01f74.png)
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解题方法
8 . 已知函数
.
(1)若
在点
处的切线方程为
,求实数
的值;
(2)设
,在(1)的条件下,若满足
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb1f610e1f0798fca75158bbe6203a0d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9f8845aa2b51c460f2d798c9f62fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9355031ea0b2dc9cef3777621bc6d38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/670a1af8b7e6d0fb88e0679db219aa14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60474077af6f9daee8bfebafcadc1081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8485e22701be2c0d84b0af8a9212e265.png)
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2023-04-22更新
|
593次组卷
|
3卷引用:贵州省六校联盟2023届高三实用性联考(四)数学(理)试题
解题方法
9 . 已知函数
(其中e是自然对数的底数),曲线
在点
处的切线方程是
,
.
(1)求a,b;
(2)若
在
上恒成立,求m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deb6c9234fb9a83f07a937428f237cb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/150e8e4ca6aa729a72a6a17c36b8ebfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef2123278fa0deabcfaf973dac14e2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7075665faaad222557aa8b6941770f65.png)
(1)求a,b;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6384364807468e0b75484c01a85a77a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
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名校
10 . 已知函数
(其中
是自然对数的底数),
.
(1)讨论函数
的单调性;
(2)若
在
上恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd5ac308e2f2a6c4eb791d47d9ab18bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4b856ad4e7c0d749151a5b9d6b97d2d.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447d6f62c09c1d05346fd16a24159f6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2023-04-13更新
|
518次组卷
|
3卷引用:贵州省黔西南州兴义市义龙蓝天学校2023届高三一模数学(文)试题