名校
1 . 一般地,设函数
在区间
上连续,用分点
将区间
分成
个小区间,每个小区间长度为
,在每个小区间
上任取一点
,作和式
.如果
无限接近于
(亦即
)时,上述和式
无限趋近于常数
,那么称该常数
为函数
在区间
上的定积分,记为
.当
时,定积分
的几何意义表示由曲线
,两直线
与
轴所围成的曲边梯形的面积.如果
是区间
上的连续函数,并且
,那么
.
(1)求
;
(2)设函数
.
①若
恒成立,求实数
的取值范围;
②数列
满足
,利用定积分几何意义,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca6d68f1de3e70696f1d5d60affe6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2779faf49c4c603fdb73ef6f03cc8d82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca6d68f1de3e70696f1d5d60affe6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9909c1172f1e48d86dd38c8c9728a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78d74528a8974c188d81391d4f158c28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d3b6ed0cf8753da31759fcdec5e2f4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e827229de8424d07fe1f5d4dfb8b0dd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32e39890697236d28d4c81e05c255fed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a107eb946e0fe41629c644b7628d5cba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca6d68f1de3e70696f1d5d60affe6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8930c962e3b094e1ee2a99c8cc44cead.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58196b9e63ec00aa1119052b6de6ae12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/024c4cff71b59cd710d9e69618ed0428.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/436ff3cf58de28b55f7605675a47d818.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca6d68f1de3e70696f1d5d60affe6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4dd421af6cde8dad1ef435eb12cc45a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d462ee178d59547f72567d59d8a6d8c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1641f83d00194762e3e5332d2620aed9.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df83a09286eae3c3d4c674065ce07bf8.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f016825fcb10e4819eb3c8af9d5841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
②数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/598da453256520641a243aba79e072d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7c9d14bfa527b5ba538cc3960e9396f.png)
您最近一年使用:0次