2001年华东师范大学数学分析试题及解答.pdf

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1、?2001?30?1?x?202xtx e dt?2xe?.?2?2ln(1)xdxx+.?3?2(cos)sinOAIyy dxxydy=+,?OA?sinyx=?O?0,0?A(,0).?4?f?222()uf xyz=+?23326xyzxyz+=?ux?0(1,1,1)P?1)?(,)zz x y=;2)?(,)zz z x=;?12?2222221xyzabc+=?2222220 xyzabc+=(0)z?.?12?()f x?(,)a b?()fx?(,)a b?.?12?1nna=?121()nnna aaa=+g gg?17?()f x?0,1?(1)0f=?1.nx?0,1?

2、2.()nf x x?0,1?17?()f x?,a b?1.,nxa b?lim();nnf x=2.,ca b?0,(),f xc+I?(c-),b?.?2001?22222222lim2lim00 xxxtxxxtxxexedteedtex+=+1lim220+=+xxtxxedte 1)21(lim222+=+xeexxx 110=+=?+=+)1()1ln()1ln(2xdxdxxx +=)1()1ln(1xxdxxx Cxxxx+=1ln)1ln(1?2=I?).22)(222xzzxzyxfxu+=xyzyzxyzyzzx221636322=.0)1,1,1(=xu?FOR xz

3、yyzyx6463=SO?).3()22)()1,1,1(222)1,1,1(fyyxzyxfxux=+=?xy?+=21),(2222byaxyxD?+=DdxdybyaxcbyaxcV222222221?21:,sin,cos2=rDabrJaryarx?=2021022)1(abrdrrrcdV =21022)1(2drrrrabc abc322=?)(xf?),(ba?Mxf)(?),(bac?),(bax?)()()()()()(cfcxfcfcfxfxfx+=+McfabM)()(?)(xf?),(bax?)(xf?),(bax?=1nna?0M?Maaan+21?nnnaMaaa

4、a+)(21?=11nnnnaMaM?=+121)(nnnaaaa?=1,1)1,0(,0limxxn?)(01)0(sup10/=?f?1=x?0?1,1(x?=)()1()(xffxf?1,1(x?+M?M=0?0)(xf?)(0)1(0)(sup10nMxxfnnx?nxxf)(?1,0 x?nxxf)(?0?1?f?,ba?,0baxM?Mxf)(?),2,1(=nnM?),2,1(,=nbaxn?nxfn)(?=)(limnnxf?,baxn?,limbacxknk=0,01K?1Kk?,);(bacxkn?=)(limnnxf?0,02KM?2Kk?Mnfk)(?21,maxKKKk=?,);(bacxkn?Mnfk)(?f?,);(bac?