2021年硕士研究生招生入学考试复试试卷

41011xx与。若xax42|x|xe1||。x11cos,xx0。设fxxxx0,,a0x0()()，fxgx设a而D表示全平面，则0,,If(x)g(yx)dxdy________.Dlimlnsinx______.x47tanxsinxlim。x3x0xlntancosxlntanxy21xyy的n1xx8x2,1x3421()()fxfx2xtan4。sinxxdx。21x04cosd。4224axxx(x0)xy200xexdx。(x1)2(xy)dxxydy02232(x)arcsinx(()设fffff。22811111(x),x](0)()[0,]fx在设ffsinxxx)228esin(xydxdy{(,)|}Dxyxy。I22xy(22)22D812xt2dy2y(x)t(1)|y。euu2lntdudx2x9y1xex。x)3220x24lnx22x3xx当。题75(x)ft)[,]()[,]Fx在abfx在ab。alim(1cosx)x。x144e2e21xarctan(x0)(x0)2(x)0a。设fxx2a012(x,f(x))()。fx若y00(x,f(x))．．00(x,f(x))00(x)．x为f0(x)．xf0aI。设Ibx1ac．blna1lnaacbx．．b1acbxlna1c．abxbarctanxxx)dxI。设I(arctanx)c．2．arctanxc(arctanx)c．2arctanxc．x．2xyxzyz11(3,1,2)。322x18y3z1321211x3y1z2．21211x18y3z13．21211x3y1z2．2121184(x)lnx(x)arcsinxf[(x)]。设f，(x)ln(6xx)f2。x(x2)yx。yx(ax)(a0)y2222V。e2xex(x0)(x0)(x)0a。设f在xxasin[sin(sinx)]1x1x1(x)(x0)()0fx在xff(0)。y90及z2设xz22。xyzdxdy42(x,y,z)设f12If(x,y,z)dvf(x,y,z)dv。196(nn2。nndx3求。(4x)223aln|1x|.(a0)y。设yxtan(ee2)x1x1。x1x4x2x[0,4]在y求。1exln(2)2xx2e2x,x0(x)ln(sin)()x0求afx在xexf2x,x0a3571(1)2n1n12482n11y2xLxxyyLxyxy4,yx及y3x2222D271(x)()0f在xfx0在x0f(x)0sinx0x22yx2y21hh2(R)V]Rh3设fx()232x0。xx(x)xf(x)x与AfCf与B(x)xf(x)xDaxa。(x)x在f(x)在设f1f(a2h)f(ah)lim[f(a)f(a)]limACBDhhhh0f(ah)f(ah)f(a)f(ah)limlim2hhh0h0()0(0),(1),(1)(0)或ff(0)(1)[0,1]上fx。ffff(1)(0)(1)(0)(1)(1)(0)(0)fffAffffBDf(1)f(0)f(1)f(0)f(1)f(0)f(1)f(0)Cfex绕z。zzezeCzeAy2B22x2y22xyx2yz3,2x4y2z5与y。ABf(x)。x0(x)0xf(x)f。022222ya(a,a)。x33344u(x,y,z)v(x,y,z)。xx当It020yz