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时间:2019-03-06
《2011-2012(1)高数a试题及答案(实验)》由会员上传分享,免费在线阅读,更多相关内容在教育资源-天天文库。
1、2011-2012学年第一学期期末考试试题(A卷)课程名称高等数学总分得分一、单项选择题(共15分每小题3分)1.下列函数在定义域内()是奇函数2x−x(A)f()xxx=()ln;(B)fx()=+ee;sinx⎛⎞ax−(C)fx()=;(D)fx()=ln⎜⎟(>0)a.x⎝⎠ax+2sin()x−12.极限lim=()x→1x−11(A)1;(B)0;(C)2;(D).2x3.x=π是函数fx()=的().tanx(A)可去间断点;(B)跳跃间断点;(C)无穷间断点;(D)振荡间断点.−−xx4、若f()x的一个原函数
2、为Fx(),则∫e(fe)dx为()x−x(A)F(e)+C;(B)−FC(e)+;−x−xF(e)(C)F(e)+C;(D)+C.x5、在MATLAB中,求函数sin(2)x在[0,1]上的定积分的命令是()(A)int(sin(2),,0,1)xx;(B)int(sin2,,0,1)xx;(C)int(sin[2∗x],0,1);(D)int(sin(2∗xx),,0,1).1、D;2、C;3、C;4、B;5、D.得分二、填空题(共15分每小题3分)21、函数f()xx=−+1lnx的定义域为.2⎧⎪x=+1t2、曲线⎨在
3、t=2处的切线方程为.3⎪⎩yt=第1页共7页−arcsinx3、设函数y=e,则dy=d(arcsinx).124、定积分∫xsinxdx=.−1x∫f()tdt05、若f()x为连续函数,且已知ff()00=,0′()=2,则lim的值为.2x→0x−arcsinx1、(0,1];2、yx=37−;3、−e;4、0;5、1.三、求解下列各题(共5小题,每小题8分,共40分)得分x⎛⎞x1.求极限lim⎜⎟.x→∞⎝⎠1+xx⎛⎞x+−11解:法一:原式=lim⎜⎟······························
4、··········································3分x→0⎝⎠1+x−x−+⋅(1x)⎛⎞11+x=−lim1⎜⎟···············································································6分x→0⎝⎠1+x1=····································································································
5、·············8分e−x⎛⎞x+1法二:原式=lim⎜⎟······················································································3分x→0⎝⎠xx⋅−(1)⎛⎞1=+lim1⎜⎟··························································································6分x→0⎝⎠x1=·····················
6、····························································································8分e得分2ydydy2.设函数yfx=()由方程xy+=ee确定,求,.2dxdxx=0x=0ddyyy解:等式两边求导得yx++=e0·························································3分ddxxdyy所以=−,··································
7、·················································4分ydexx+第2页共7页d1y因为x=0,y=1,所以=−····························································5分dexx=0yyddyy2(e)xy+−(1e+⋅)dyddxx所以=−22yd(xx+e)2dy2所以x=0,=−e·································································
8、···········8分2dx得分2x3.证明:当x>0时,ln(1+>−xx).22x证明:设fx()ln(1)=+−+xx,·····································································2分22
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