1 . 已知平方和公式:
,其中
.
(1)记
,其中
,求
的值;
(2)已知
,求自然数
的值;
(3)抛物线
.
轴及直线
围成了如图(1)的阴影部分,
与
轴交于点
,把线段
分成
等份,作以
为底的内接矩形如图(2),阴影部分的面积为
,
等于这些内接矩形面积之和.
,当
时的极限值.
![](https://img.xkw.com/dksih/QBM/2020/8/6/2522228892000256/2522958075985920/STEM/57322956baba4cdebe449f79eeb00cfd.png?resizew=610)
图(3)中的曲线为开口向右的抛物线
,抛物线
.
轴及直线
围成了图中的阴影部分,请利用极限平方和公式.反函数或割补法等知识求出阴影部分的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c698639cdba709641d3c91ea1798abfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
(1)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb5d8ebd8544c7c90f5772eb7185498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1edd770d288fa52a742d73ef9d5edae7.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3735968325345a8f5a23bbb2723354a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13cf1ba54a1d09dcd2fd68add8a107bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab9057a085e325652e874898b69aa0a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89846a5f66a8f9259a0b07cae9776084.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cc3ec69887a76bfb07531b5d5745255.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49d154b00d2363a51a93657d941f07ff.png)
![](https://img.xkw.com/dksih/QBM/2020/8/6/2522228892000256/2522958075985920/STEM/57322956baba4cdebe449f79eeb00cfd.png?resizew=610)
图(3)中的曲线为开口向右的抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e8953ded144195804384dcb494d5e2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aef469c7b7cb9945b984222381b9c000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ff51fab7db7694fab8b42aa4f1bf295.png)
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2 . (1)求函数
的导数;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8fe3eedd655e22aa824d4e99aadebc1.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0206f8827097efb62fc11c3cd045a436.png)
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