暨南大学-06-高等数学A试题及答案(经管)-微积分下

第1页共6页暨南大学考试试卷得分评阅人一、填空题（共8小题，每小题3分，共24分）1.1.1.1.下列函数fxfxfxfx====()3()3()3()3,,,,xxxxfxxfxxfxxfxx=+=+=+=+2222()(1)()(1)()(1)()(1),,,,xxxxfxxfxxfxxfxxxxxx⎧⎧⎧⎧⎪⎪⎪⎪========⎨⎨⎨⎨⎪⎪⎪⎪−−−−⎩⎩⎩⎩1,01,01,01,0()0,0()0,0()0,0()0,01,01,01,01,0,,,,xxxxxxxxfxfxfxfxxxxxxxxx≥≥≥≥⎧⎧⎧⎧====⎨⎨⎨⎨−−−−⎩⎩⎩⎩,0,0,0,0()()()(),0,0,0,0中,,,,初等函数的个数是33332222....3333x+x+5=0x+x+5=0x+x+5=0x+x+5=0实根的个数是11113.3.3.3.曲线nnnnf(x)xf(x)xf(x)xf(x)x====在点(,)(,)(,)(,)11111111处的切线与xxxx轴交点为(((())))nnnn,,,,ξξξξ0000,,,,则nnnnnnnnlimf()limf()limf()limf()ξξξξ→∞→∞→∞→∞====eeee−−−−11114.4.4.4.xdxxdxxdxxdx−−−−∫∫∫∫333300001111====255.5.5.5.xxxxxxxxxxxxfxfxfxfxxxaxxxaxxxaxxxax⎧⎧⎧⎧⎪⎪⎪⎪++++====⎨⎨⎨⎨⎪⎪⎪⎪−+≤−+≤−+≤−+≤⎩⎩⎩⎩2222sin2sin2sin2sin2,0,0,0,0ln(1)ln(1)ln(1)ln(1)()()()()32,032,032,032,0连续，则a====26666....若ykxykxykxykx====tan2tan2tan2tan2的一个原函数为xxxx2222lncos2lncos2lncos2lncos23333，则kkkk=34−教师填写20_06-20_07学年度第___1___学期课程名称：_高等数学1(经管内招生)_授课教师姓名：_苏保河，吴广庆，邹泽民_考试时间:___2007___年___01___月________日课程类别课程类别课程类别课程类别必修必修必修必修[[[[√√√√]]]]选修选修选修选修[[[[]]]]考试方式考试方式考试方式考试方式开卷开卷开卷开卷[[[[]]]]闭卷闭卷闭卷闭卷[[[[√√√√]]]]试卷类别试卷类别试卷类别试卷类别(A(A(A(A、、、、B)B)B)B)[[[[AAAA]]]]共共共共6666页页页页考生填写学院(校)专业班(级)姓名学号内招内招内招内招[[[[]]]]外招外招外招外招[[[[]]]]题号一二三四五六七八九十总分得分暨南大学《高等数学1(经管内招生)》试卷A考生姓名、学号：第2页共6页7.7.7.7.设gxgxgxgx()()()()可导且gggggggg′′′′========(0)(0)0(0)(0)0(0)(0)0(0)(0)0，1000gxxgxxgxxgxxxxxxxxxxfxfxfxfx⎧⎧⎧⎧≠≠≠≠⎪⎪⎪⎪⎨⎨⎨⎨⎪⎪⎪⎪====⎩⎩⎩⎩====()sin()sin()sin()sin,,,,()()()()，则0ffff′′′′====()()()()00008888....xxxxyyyyxxxxxxxx−−−−====−+−+−+−+22222222111132323232，则y的可去间断点是x1x1x1x1====得分评阅人二、单项选择题（共9小题，每小题3分，共27分）1.1.1.1.设(((())))fxfxfxfx是连续函数且为奇函数，则函数xxxx0000f(t)dtf(t)dtf(t)dtf(t)dt∫∫∫∫是::::【B】.(A).(A).(A).(A).奇函数(B).(B).(B).(B).偶函数(C).(C).(C).(C).非奇非偶函数....(D).(D).(D).(D).非连续函数....2.2.2.2.设f(x)f(x)f(x)f(x)有连续的导数，则2fxdxfxdxfxdxfxdx′′′′====∫∫∫∫()()()()【C】.(A).(A).(A).(A).fxCfxCfxCfxC++++()()()()....(B).(B).(B).(B).2fxCfxCfxCfxC++++()()()()....(C).(C).(C).(C).122fxCfxCfxCfxC++++()()()()....(D).(D).(D).(D).12fxCfxCfxCfxC++++()()()()3.3.3.3.222xxxxdxdxdxdxxxxxxxxx−−−−++++∫∫∫∫sinsinsinsincoscoscoscos====【B】.(A)(A)(A)(A)1....(B)(B)(B)(B)0....(C)(C)(C)(C)1−....(D)(D)(D)(D)22224.4.4.4.1211dxdxdxdxxxxx−−−−∫∫∫∫====【D】.(A)(A)(A)(A)2....(B)(B)(B)(B)1....(C)(C)(C)(C)2−....(D)(D)(D)(D)不存在5.5.5.5.当1x→−时，与()1321x+−等价的无穷小量是::::【A】.（AAAA）....sin(1)3x+....（BBBB）....13x−；（CCCC）....1x+；（DDDD）....sin(1)x+。6.6.6.6.（0,00,00,00,0）是曲线ｙ＝ｘ3的::::【A】.（AAAA）拐点，（BBBB）间断点，（CCCC）极值点，（DDDD）无切线之点7.7.7.7.极限xxxxxxxxlimlimlimlim−−−−→→→→====1111111111115555【C】.暨南大学《高等数学1(经管内招生)》试卷A考生姓名、学号：第3页共6页（AAAA）+∞+∞+∞+∞；（BBBB）0;;;;（CCCC）不存在，且不是+∞+∞+∞+∞；（DDDD）11118.8.8.8.设xxxxfxaaafxaaafxaaafxaaa=≠=≠=≠=≠()(0,1)()(0,1)()(0,1)()(0,1),,,,则[[[[]]]]nnnnfffnfffnfffnfffnnnnn→∞→∞→∞→∞====22221111limln(1)(2)...()limln(1)(2)...()limln(1)(2)...()limln(1)(2)...()【A】.(A).(A).(A).(A).aaaa1111ln.ln.ln.ln.2222(B).(B).(B).(B).aaaa2ln.2ln.2ln.2ln.(C).(C).(C).(C).aaaa1111....lnlnlnln(D).(D).(D).(D).aaaa2222....lnlnlnln9.9.9.9.下列命题错误的是【C】.(A).(A).(A).(A).若xxxxxxxxlimf(x)alimf(x)alimf(x)alimf(x)a→→→→====0000,,,,则xxxxxxxxlimf(x)alimf(x)alimf(x)alimf(x)a→→→→====0000；((((B).B).B).B).若()fx在0x处连续，则()fx在0x处也连续；((((C)C)C)C)....若()fx在0x处可导，则()fx在0x处也可导；(D)(D)(D)(D)....若()fx在[],ab上可积，则()fx在[],ab上也可积。得分评阅人三、计算题（共6小题，每小题5分，共30分）1.1.1.1.0111xxxxxxxxlim.lim.lim.lim.xxxxeeee→→→→⎛⎞⎛⎞⎛⎞⎛⎞−−−−⎜⎟⎜⎟⎜⎟⎜⎟−−−−⎝⎠⎝⎠⎝⎠⎝⎠解：0111xxxxxxxxxxxxeeee→→→→⎛⎞⎛⎞⎛⎞⎛⎞−−−−⎜⎟⎜⎟⎜⎟⎜⎟−−−−⎝⎠⎝⎠⎝⎠⎝⎠limlimlimlimxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxexeexeexeexelimlimlimlimlimlimlimlimx(e)eexex(e)eexex(e)eexex(e)eexe→→→→→→→→−−−−−−−−−−−−========−++−++−++−++00000000111111111111…………………………………………..3..3..3..3分xxxxxxxxxxxxxxxxxxxxeeeelimlimlimlimeexeeexeeexeeexe→→→→========++++++++000011112222…………………………………………..5..5..5..5分2.2.2.2.nnnnnnnni1i1i1i11n+i1n+i1n+i1n+ilim.lim.lim.lim.nnnnnnnn→∞→∞→∞→∞====∑∑∑∑暨南大学《高等数学1(经管内招生)》试卷A考生姓名、学号：第4页共6页解：nnnnnnnn11110000nnnnnnnni1i1i1i1i1i1i1i11n+i1i1n+i1i1n+i1i1n+i1ilimlim11xdxlimlim11xdxlimlim11xdxlimlim11xdxnnnnnnnnnnnnnnnn→∞→∞→∞→∞→∞→∞→∞→∞=========+=+=+=+=+=+=+=+∑∑∑∑∑∑∑∑∫∫∫∫……………………..3..3..3..3分(((())))22222212212212213333=−=−=−=−……………………...5...5...5...5分3.3.3.3.1111xysiny0xysiny0xysiny0xysiny02222−+=−+=−+=−+=,,,,求dydydydydxdxdxdx解：11111yycosy01yycosy01yycosy01yycosy02222′′′′′′′′−+=−+=−+=−+=…………………………………………..3..3..3..3分dy2dy2dy2dy2dx2cosydx2cosydx2cosydx2cosy====−−−−…………………………………………..5..5..5..5分4.4.4.4.22xxxxtttt2x2x2x2xyesintdtyesintdtyesintdtyesintdt−−−−====∫∫∫∫,,,,求dy解：42424242x24xx24xx24xx24xdy[2xesinx-(-2)esin(2x)]dxdy[2xesinx-(-2)esin(2x)]dxdy[2xesinx-(-2)esin(2x)]dxdy[2xesinx-(-2)esin(2x)]dx=−=−=−=−………………………………..3..3..3..3分42424242x24xx24xx24xx24x(2xesinx-2esin2x)dx(2xesinx-2esin2x)dx(2xesinx-2esin2x)dx(2xesinx-2esin2x)dx====………………………………..5..5..5..5分5.5.5.5.22221lnx1lnx1lnx1lnxdxdxdxdx43(xlnx)43(xlnx)43(xlnx)43(xlnx)++++++++∫∫∫∫暨南大学《高等数学1(经管内招生)》试卷A考生姓名、学号：第5页共6页解：22221lnx1lnx1lnx1lnxdxdxdxdx43(xlnx)43(xlnx)43(xlnx)43(xlnx)++++++++∫∫∫∫22221d(3xlnx)1d(3xlnx)1d(3xlnx)1d(3xlnx)34(3xlnx)34(3xlnx)34(3xlnx)34(3xlnx)====++++∫∫∫∫………………………………..3..3..3..3分333322221111arctan(xlnx)Carctan(xlnx)Carctan(xlnx)Carc