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2002∞=∫.1.()21011.lnln|eedxxxx+∞+∞=−=−−=∫2()yyx=2610yexyx++−=()''0y=.2.xyx''6620,yeyxyyx+++=1xy'yx()2''''''61220,yyeyeyxyy++++=20x=0,y=0x=0y=1()'0y=02()''0y=2.3'''20yyy+='0011,2||xxyy====.1yx=+21yx=+'yp=''',dydpdpdydpypdxdxdydxdy=====2002=0p=0dyyppdp+='012|xy==0dyyppdp+=1,pyC=1.dyyCdx='0011,2||xxyy====112C=1,2dyydx=12ydy=22.yxC=+01|xy==21C=.21yx=+1yx=+4()()222123123121323,,444fxxxaxxxxxxxxx=+++++xPy=216,fy=a=.2.1()()222123123121323,,444fxxxaxxxxxxxxx=+++++2222,22aAaa⎡⎤⎢⎥=⎢⎥⎢⎥⎣⎦216fy=600000.000B⎡⎤⎢⎥=⎢⎥⎢⎥⎣⎦,AB,ABA600.2002()()222222242aEAaaaaλλλλλλ−−−−=−−−−−−=−+−−⎡⎤⎡⎤⎣⎦⎣⎦46,20,aa+=−=a=22,ABEAEBλλ−=−226002200,2200aaaλλλλλλ−−−−−−−=−−−()()()()()232232232426334426,aaaaaaλλλλλλλλλ−+−−=−⎡⎤⎡⎤⎣⎦⎣⎦−+−−+−=−a=25X()()2,0Nµσσ240yyX++=12µ=.4240yyX++=40X−.{}142PX={}{}14414124411XPXPXPXPYPµµσσµµµσσσ−−⎧⎫==−≤=−≤⎨⎬⎩⎭−−−⎧⎫⎛⎞⎧⎫=−≤=−Φ⎨⎬⎨⎬⎜⎟⎩⎭⎝⎠⎩⎭2002()22112txdtxeπ−−∞=−Φ=∫41404.2µµµσσ−−⎛⎞Φ=⇒=⇒=⎜⎟⎝⎠1(),fxy4(),fxy()00,xy(),fxy()00,xy(),fxy()00,xy(),fxy()00,xy.PQ⇒PQA⇒⇒B⇒⇒C⇒⇒D⇒⇒A(),fxy()00,xy(),fxy()00,xy⇒⇒A.2()01,2,3,nun≠=Llim1,nnnu→∞=()111111nnnnuu∞+=⎛⎞−+⎜⎟+⎝⎠∑.(A)BCD.Clim1,nnnu→∞=2002→∞→∞=⋅=n()()11223341111111111111111nnnnnnSuuuuuuuuuu++++⎛⎞⎛⎞⎛⎞⎛⎞=+−+++++−+⎜⎟⎜⎟⎜⎟⎜⎟⎝⎠⎝⎠⎝⎠⎝⎠=+−L11limnnSu→∞=AD()1111111111nnnnnnnuuuu∞∞+==⎛⎞⎛⎞−+=+⎜⎟⎜⎟++⎝⎠⎝⎠∑∑1limlim1,1nnnnunun→∞→∞==1111limlim1,11nnnnunun+→∞→∞++==+11111,,nnnnuu∞∞==+∑∑1111nnnuu∞=⎛⎞+⎜⎟+⎝⎠∑()111111nnnnuu∞+=⎛⎞−+⎜⎟+⎝⎠∑C3()yfx=()0,+∞A()lim0xfx→+∞=()'lim0xfx→+∞=B()'limxfx→+∞()'lim0xfx→+∞=C()0lim0xfx+→=()'0lim0xfx+→=D()0lim0xfx+→=()'0lim0xfx+→=B1()2sin,xfxx=()0lim0xfx+→=()fx()0,+∞2002()2222'2222cossinsin2cosxxxxfxxxx−==−()fx()0,+∞()'limxfx→+∞()'0lim10xfx+→=≠AD()sinfxx=()fx()0,+∞()0lim0xfx+→=()'00limlimcos10xxfxx++→→==≠CB.2B()'limxfx→+∞()'lim0,xfxA→+∞=≠0A2Aε=00XxX()'.2AfxAε−=()'222AAAAfxA=−+()'2Afx[],Xx()()()()()()''2AfxfXfxXfXxXζ=+−+−()fx()0,+∞()'lim0xfx→+∞=4123,1,2,3,iiiiaxayazbi++==2B2002=⎧⎪++=⎨⎪++=⎩2ACDB.51X2X()1fx()2fx()1Fx()2FxA()()12fxfx+.B()()12fxfx.C()()12FxFx+D()()12FxFx.D()()()()12122,21,fxfxdxFF+∞−∞+=≠+∞++∞=≠⎡⎤⎣⎦∫AC()1,00,0xexfxx−⎧=⎨≤⎩()222,00,0xexfxx−⎧=⎨≤⎩()()3122,00,0xexfxfxx−⎧=⎨≤⎩BD.()()12FxFx.()fx0x=()()'00,00,ff≠≠()()()20afhbfhf+−0h→h,ab.12002()()()020lim0hafhbfhfh→+−=()()()()()0lim20100.hafhbfhfabf→+−=+−=⎡⎤⎣⎦()00,f≠10ab+−=()()()()()()()'''0020220limlim201hhafhbfhfafhbfhabfh→→+−+===+()'00,f≠20,ab+=2,1ab==−2()()()()()()()()()()00200lim020000lim2hhafhbfhfhafhfbfhfafbffhhh→→+−=⎧⎫−−⎡⎤⎡⎤+−⎪⎪⎣⎦⎣⎦=++⎨⎬⎪⎪⎩⎭3()()()()()000100afbffabf+−=+−=10ab+−=()()()()()()()()()()()00'''200lim020lim202020hhafhbfhfhafhfbfhfhhafbfabf→→+−=⎧⎫−−⎡⎤⎡⎤⎪⎪⎣⎦⎣⎦=+⎨⎬⎪⎪⎩⎭=+=+20ab+=2,1ab==−2002()2arctan0,xtyfxye−==∫()0,02limnnfn→∞⎛⎞⎜⎟⎝⎠()00f=()()2arctan'2001,1|xxefx−===+,yx=()()'202limlim2202.2nnffnnffnn→∞→∞⎛⎞−⎜⎟⎛⎞⎝⎠=⋅==⎜⎟⎝⎠()22max,,xyDedxdy∫∫(){},|01,01Dxyxy=≤≤≤≤(){}(){}12,|01,0,|01,1DxyxyxDxyxxy=≤≤≤≤=≤≤≤≤()()()2222221222221122max,max,max,11000011001xyxyxyDDDxyxyxyDDxyedxdyedxdyedxdyedxdyedxdydxedydyedxxedxyedye=+=+=+=+=−∫∫∫∫∫∫∫∫∫∫∫∫∫∫∫∫()fx(),−∞+∞L()0y(),ab(),cd()()222111LxIyfxydxyfxydyyy⎡⎤⎡⎤=++−⎣⎦⎣⎦∫2002=I.1()()()()2'2221111xyfxyfxyxyfxyxyyyfxyyy⎧⎫∂⎡⎤−=−+⎨⎬⎣⎦∂⎩⎭⎧⎫∂⎡⎤=+⎨⎬⎣⎦∂⎩⎭IL2IL(),ab(),cb(),cd()()()()()()()222111cdabcdabbcadabbcadabcIbfbxdxyfcydybycaccbfbxdxcfcydybdbcaftdtftdtdbcaftdtdb⎡⎤⎡⎤=++−⎣⎦⎣⎦−=+++−=−++=−+∫∫∫∫∫∫∫abcd=()0,adabftdt=∫caIdb=−1()()()369313!6!9!3!nxxxxyxxn=++++++−∞+∞LL''';xyyye++=21()303!nnxn∞=∑.1()()()()369325831'1,3!6!9!3!,2!5!8!31!nnxxxxyxnxxxxyxn−=++++++=+++++−LLLL2002()()4732'',4!7!32!nxxxyxxn−=+++++−LL23'''1;2!3!xxxyyyxe++=++++=L2'''0yyy++=210λλ++=1,21322iλ=−±1a=*xyAe=*y'''yyy++=xe1,3A=*13xye=2212133cossin322xxxyeCexCex−−=++()yx()()'01,00.yy==122,0.3CC==()2123cos332xxyeexx−=+−∞+∞xOy(){}22,|75Dxyxyxy=+−≤()22,75hxyxyxy=−−+.1()00,MxyD(),hxy()00,gxy()00,gxy.2D2275xyxy+−=(),gxy2002()()()()()000000220000220000,2222558Mgxygradhyxixyjyxxyxyxy==−+−=−+−=+−2()00,gxy220000558xyxy+−()()222,,558fxygxyxyxy==+−()()()22,,,558Fxyfxyxyxyλλ=++−()()2210820(1)10820(2)750FxyyxxFxyyxyFxyxyλλλ∂=−+−=∂∂=−+−=∂∂=+−−=∂(3)12()()20.xyλ+−=,yx=−2λ=2λ=1yx=353,53xy=±=±,yx=−35,5xy=±=m4()()()()12345,5;5,5;53,53;53,53.MMMM−−−−()()()()1234450;150.fMfMfMfM====1M2M.2002()1234,,,Aαααα=1234,,,αααα4234,,ααα1232ααα=−1234βαααα=+++Axβ=.11234xxxxx⎡⎤⎢⎥⎢⎥=⎢⎥⎢⎥⎣⎦112233441234xxxxαααααααα+++=+++1232ααα=−()()()122133442310xxxxxααα+−+−++−=234,,ααα12134230010xxxxx+−=⎧⎪−+=⎨⎪−=⎩0132,0110xk⎧⎫⎧⎫⎪⎪⎪⎪−⎪⎪⎪⎪=+⎨⎬⎨⎬⎪⎪⎪⎪⎪⎪⎪⎪⎩⎭⎩⎭k.2234,,ααα123420αααα=−+A30Ax=.1234200αααα−++=1210⎧⎫⎪⎪−⎪⎪⎨⎬⎪⎪⎪⎪⎩⎭0Ax=,2002⎧⎫⎪⎪−⎪⎪=⎨⎬⎪⎪⎪⎪⎩⎭k.()12341