1 . 如图,在四棱锥
中,底面
为正方形,
平面
,
,
为
的中点,
为棱
上一动点.
(1)
在棱
上何处时,可使得
平面
?并证明你的结论;
(2)求证:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbfbaf73297240eb116f22489519895a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/17/58b45cc1-be6e-47ed-82d2-fd6e4b978dab.png?resizew=155)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6501f1c913a4ef64957a2f01ab5baa15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2 . (1)已知a、b、c是不全相等的正数,且
.求证:
.
(2)用反证法证明:若函数
在区间
上是增函数,则方程
在区间
上至多只有一个实数根.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca542e78b7d77d008c9c4752afa91a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa54caec3efb5765d189b06789c336ad.png)
(2)用反证法证明:若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3047d4ab078dafc06c047bcbf0a6ffaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
您最近一年使用:0次
名校
3 . (1)已知
,
,
,求证:
.
(2)用分析法证明:对于任意
时,有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061813f1ec633c5c4c393c4de7938322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5558c083d34cbb0a58d3ce1dc6f5778e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/128294be1f10b83df30ad60d4c696224.png)
(2)用分析法证明:对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6964979a90a2036e9dd541c40cb50be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e8010392b125fb5f015992bad5d6fa.png)
您最近一年使用:0次
名校
解题方法
4 . (1)已知x,y>0,且x+y>2.求证:
中至少有一个小于2;
(2)设a,b,c>0且不全相等,若abc=1,证明:a2(b+c)+b2(c+a)+c2(a+b)>6.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c07f0aced5b76fbb5464e7309de2d152.png)
(2)设a,b,c>0且不全相等,若abc=1,证明:a2(b+c)+b2(c+a)+c2(a+b)>6.
您最近一年使用:0次
解题方法
5 . 如图,在直三棱柱
中,已知
,设
的中点为
,
.求证:
![](https://img.xkw.com/dksih/QBM/2020/8/14/2527831942242304/2530675692716032/STEM/5843b21c-e222-4d2c-8df9-5e1d4f551b9e.png)
(1)
平面
(指出所有大前提、小前提、结论);
(2)
(用分析法证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eec2bbb7272f66c7cf92620da8372d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88b866f54e2c5c1df06364cdc7eb59bc.png)
![](https://img.xkw.com/dksih/QBM/2020/8/14/2527831942242304/2530675692716032/STEM/5843b21c-e222-4d2c-8df9-5e1d4f551b9e.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98faac7a82235d53bb4b6abe7ee54951.png)
您最近一年使用:0次
解题方法
6 . 已知椭圆
的离心率为
,两焦点之间的距离为4.
(1)求椭圆的标准方程;
(2)过椭圆的右顶点作直线交抛物线
于A、B两点,
①求证:OA⊥OB;
②设OA、OB分别与椭圆相交于点D、E,过原点O作直线DE的垂线OM,垂足为M,证明|OM|为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/948261c41cc1509f023761d880c75582.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求椭圆的标准方程;
(2)过椭圆的右顶点作直线交抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
①求证:OA⊥OB;
②设OA、OB分别与椭圆相交于点D、E,过原点O作直线DE的垂线OM,垂足为M,证明|OM|为定值.
您最近一年使用:0次
2020-07-30更新
|
128次组卷
|
2卷引用:甘肃省武威第八中学2019-2020学年第二学期期末考试高二数学(文科)试卷
名校
7 . (1)求证:
.
(2)已知
,用分析法证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/791586b58c62684f6983a12c14300bdd.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ac12138178cb539a9e1c8f77587038.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd0bbac8f3e00fd58c206d93a20a3f92.png)
您最近一年使用:0次
2020-02-26更新
|
382次组卷
|
2卷引用:甘肃省天水市甘谷县第一中学2019-2020学年高二上学期期末数学(文)试题
8 . 在数列
中,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61fe23549697a06a4cb825b7cf8edf66.png)
(1) 求证:
;
(2)若
,求
的值,观察并猜想出数列已知数列
的通项公式
,并用数学归纳法证明你的猜想.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa01f03fb074bff35b35e07047d11b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61fe23549697a06a4cb825b7cf8edf66.png)
(1) 求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c653177884385ae15b71438aac4e704d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5b862c625e9afa23d5790b08dd3516d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
您最近一年使用:0次
2019-05-14更新
|
468次组卷
|
3卷引用:【全国百强校】甘肃省白银市会宁县第四中学2018-2019学年高二下学期期中考试数学试题
【全国百强校】甘肃省白银市会宁县第四中学2018-2019学年高二下学期期中考试数学试题河南省洛阳市2018-2019学年高二下学期期中考试数学试题(理)(已下线)考点57 推理与证明-备战2021年高考数学(理)一轮复习考点一遍过
名校
9 . 证明下列不等式:
(1)用分析法证明:
;
(2)已知
是正实数,且
,求证:
.
(1)用分析法证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14c19d94ff48082c1cd213c82c99abf0.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751e274e9107d780c39ba9c49d6daefb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d689b0da0bd4803b3e8a6c69542ae466.png)
您最近一年使用:0次
10 . 已知△ABC的三边长为a,b,c,三边互不相等且满足b2<ac
(1)比较
与
的大小,并证明你的结论;
(2)求证:B不可能是钝角.
(1)比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61fe34b1cc3a3cfcfad66fb03b9e22c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c147d6cbd7cbaeb8ec08a0ba69cd59dd.png)
(2)求证:B不可能是钝角.
您最近一年使用:0次