2018考研数学一参考答案一、选择题1.D2.B3.B4.C5.A6.A7.A8.D二、填空题9.-210.22ln211.ki12.013.-114.41三、解答题15.解:xxxxdeedxee221arctan211arctanCeeeeCeeeeedeeeedeeeeedxeeeedxeeeeeexxxxxxxxxxxxxxxxxxxxxxxxxxxx121)1(611arctan2112)1(32411arctan21)1(111411arctan21111411arctan211411arctan21)1(112211arctan2123223222222216.解:设圆的周长为x,正三角周长为y,正方形的周长为z,由题设2zyx,则目标函数:163634)4()3(23212222222zyxzyxS)(,故拉格朗日函数为)2(163634,,,222zyxzyxzyxL)(则:02xLx03632yLy0162zLz02zyxL解得4331,4338,433364332zyx,.此时面积和有最小值4331S.17.解:构造平面0133:'22xzy,取后侧,设'和所围区域为;记;,,33zRzyQxP借助高斯公式,有:4514)31(34)31(523)31()31(2313)31()231(313)31()31(31)61(2)31(31)331(331)331()331(0-31212252231021223223102222310222031023222223233102222''''12212222rrrdrrrdrrrdrrrdrrrddydzzyzydxzydydzdxdydzzydxdyRQPRdxdyQdzdxPdydzRdxdyQdzdxPdydzRdxdyQdzdxPdydznzynzyzyzyx)(18.(1)解:通解大型考试资源分享网站百度搜索:华宇课件网http://www.china-share.com-更多热门考试学习资源免费下载--出售:公考、考研、会计、建筑、教师等考试课程-课程咨询微信QQ同号:582622214xzxxxdxdxCexCexeCdxxeeCdxxeexy)1()1()()()((2)证明:设的周期是即)()(),(xfTxfTx通解论得证依旧是方程的通解,结即则有不妨设)()()()()()()()()()()(,)()()(])([])([)(200u)(0)()()(0TxyeCedueufeeCedueeufeeCeTudeTufeCeTxdeTxfeTxyCedxexfexyeCdxexfeCdxexfeCdxexfexyxyuxxxTyyxxxTTuTxTxxyxTxTxxxxxxxxxxdxdx...