高职高等数学试题库H卷

第1页共5页学院、系专业班级学号姓名············································密································封·······························线···································山东英才学院学年第一学期《高等数学》期末模拟考试一年级专业层次：普通高职普通本科（本试卷考试时间120分钟满分100分）一、单选题（每题3分，共18分）1．函数29yx的定义域是（）()33;()33;()3;()3.AxxBxCxDx或2．0sin2limxxx（）1();()2;()0;()2ABCD3．设ln||yx，则'y=（）1111();();();()||||ABCDxxxx4．设函数xexf2，则不定积分dxxf等于（）()ACex221()BCex22()CCex2()DCex25．设coslnyxx，则'xy（）()A1()B1()C2()D6．2sincosxxdx=（）题号一二三四五总分复核得分得分阅卷人√第2页共5页333311()cos;()cos;3311()sin;()cos33AxCBxCCxCDx二、填空题（每题3分，共18分）7．2ln(1)lim2xxx_________________；8．设sinyx，则y=____________________；9．设cos2yx，则dy=___________________；10．sinxxdx；11．221xdxx；12．函数11)(2xxxf的间断点是。三、计算题（共52分）13．（5分）计算：4lim(1)xxx14．（5分）已知''()tan(),()22xfxfxf，求得分阅卷人得分阅卷人第3页共5页学院、系专业班级学号姓名············································密································封·······························线···································15．（6分）由方程sincos()0yxxy确定y为x的函数，求02|xydydx16．（6分）求抛物线2yx在1,1处的切线方程和法线方程。17．（6分）arctan2lim1xxx。第4页共5页18．（6分）求不定积分：2sin()xxdx19．（6分）求函数32()2312fxxxx在[3,4]上最大值和最小值。20．（6分）求不定积分：lnxxdx21．（6分）求不定积分：21xdx第5页共5页学院、系专业班级学号姓名············································密································封·······························线···································四、应用题（共6分）22．欲用长6lm的木料加工一日字形的窗框，问它的边长和边宽分别为多少时，才能使窗框的面积最大？最大面积为多少？五．证明题（共6分）23．证明方程sin10xx在0与之间有实根。得分阅卷人得分阅卷人