高等数学基本概念

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fydstudio@live.cn1/78fydstudio@live.cn§1.1)1.00()(0)()2()()aaafxafxdxfxdxfx(1)2.(a,b()0fx()fx()0fx()fx(2)11521[()ln(1)].xxIxxeexxdx1()xxfxee2112()(),()ln(1)xxfxeefxfxxx22222(1)()ln(1)ln1xxfxxxxx22ln1ln(1)()xxfx2()ln(1)xxxeexx1166102027Ixdxxdx2()()Fxfx(A)()fx()Fx(B)()fx()Fx(C)()fx()Fx(D)()fx()Fx(B)32(),()13xfxxFx(C)()cos1,()sinfxxFxxx(D)2()2,()(,)fxxFxx(A)2/78fydstudio@live.cn0()(0)(),xFxFftdtf000()(0)()(0)()()(0)()()xxxFxFftdtFfuduFfuduFx()Fx3()fx()gx()()()()0fxgxfxgxaxb(A)()()()()fxgbfbgx(B)()()()()fxgafagx(C)()()()()fxgxfbgb(D)()()()()fxgxfaga2()1[()()()()]0()()fxfxgxfxgxgxgx()()fxgxx()()()()fxfbgxgb(A)1.()fx()gx[()]fgx2.[()]fgx()gx()fx12()()()fxxafxfxxa12()()()gxxbgxgxxb[()]fgx111122211222[()]()[()]()[()][()]()[()]()fgxxbgxafgxxbgxafgxfgxxbgxafgxxbgxa()xxfexe(1)0f()fxxetlnxtln()()xtfeftt1ln()(1)xtfxfdtt3/78fydstudio@live.cn2121ln21ln2xtx§1.21.2.3.1xxxx30sinsinlim613cos1limsinlim2030xxxxxxx2x(1-cosx)ln(1+x2xsinxnxsinxn12xe(A)1(B)2(C)3(D)44221)1ln(cos1xxx211sin2xexxxxnn4n+12n+1=3,n=2(B)3dttxdtttxtxx150sin0)1()(,sin)(x)(x)(x()(A)(B)(C)(D)exxxxxxxxxxxx5cos)sin1(555sinlim''limlimsin10004/78fydstudio@live.cn(C)121)3(,3011nnnxxxxnxx0lim232)3()3(0,03,01111211xxxxxxx)n1230nx}{nxn1)3()3(1nnnnnnnnxxxxxxxx03)23(nnnnxxxxnnxx1nxlxnnlim)3(1nnnxxx0,3,)3(22lllllll()23l23limnnx(3)2)212654321(limnnn1225432),212654321(nnynnxnn5/78fydstudio@live.cn0xnyn12102nyxxnnn0lim2nxx1sinlim0xxxennn)11(limeuuu)11(limevvv10)1(lim1nnxxx2cos4cos2coslimx=0=1xnnnnnnxxxxx2sin22cos4cos2cos2sin2lim=nnnnnnxxxxx2sin22sin2cos4cos2cos2lim111=xxxxxxxxnnnnnnsin2sin2sinlim2sin2sinlim)12sin2lim(nnnxx2)(xf),(exfx)('lim6/78fydstudio@live.cn)]1()([lim)(limxfxfcxcxxxxc:cccxxxxxeeexcxccxcx2)1()1(lim)(lim)(')]1()[(')1()(fxxfxfxf(x-1)xefxfxfxx)('lim)]1()([lim)(e2c=e,2c=121c(4)“00““0·“1“000(5)“00““0·100lnlimlnlimxxxxxx“)1()1(lim)111(lim00xxxxxexxeex“00“1“000)()(lim*xgxxf)()]([xgxf(6)7/78fydstudio@live.cn)(ln)()](ln[)()()]([xfxgxfxgeexfxg,)(ln)(lim*xfxgxe,)(ln)(lim*xfxgx“0·xxxxxxxeexxln0ln00limlimlim=10lnlimlnlim100eeexxxxxx1)cossin1(lim2220xxxx=xxxxxx222220sincossinlim=42202sin41limxxxx=3042cos2sin442limxxxxx=3024sin41limxxxx=2064cos1limxxx=xxx124sin4lim0=342)(xf0)0(fxxxdttxfxdttftx000)()()(lim=xxxxduufxdtttfdttfx0000)()()(limutx)8/78fydstudio@live.cn=)()()()()(lim000xxfduufxxfxxfdttfxxx()=)()()(lim)0(0xxfxfxfxx)=21)0()0()0(fff.(7))(]')([xfdttfxa()(xf)3a0,b0nnnxba2limxxxxba)2(lim11“1]2ln)[ln(ln,)2(1111xxxxxbaxybayxbayxxxx12ln)ln(limlnlim11)00(2ln)ln(lim10tbatxttt=abbababbaatttttln)ln(ln21lnlnlim0abbaxxxx)2(lim11abbannnn)2(lim(8)9/78fydstudio@live.cn)||sin12(lim410xxeexxx112)sin12(lim410xxeexxx110)sin12(lim4340xxeeexxxx1)||sin12(lim410xxeexxx(9))(xfyxysin)2(limnnfn0)0(f1|)'(sin)0('0xxf2)0('202)0()2(2lim)2(limfnfnfnnfnx101)()(1limdxxfnkfnnkn()(xf)1nknknn122lim10/78fydstudio@live.cn122122222nnknnnnnnk21lim222nnnn11lim222nnnnknnknnknknn12122)(111limlim=4|arctan110102xxdx2knnkn1sinlimnknknknknknnknkn111sin11sinsin112sinsin1lim101xdxnknnkn2)sin1)(1(limsin11lim11nknnknnknnnnknnknknnk121sinlim(10)13)1sin(lim221xbaxxxb.11/78fydstudio@live.cn0)(lim21baxxx1+a+b=0322)1cos(22lim)1sin(lim21221axxaxxbaxxxx5,4ba)(xf(0)(xf01)(limxfxxhhexfhxxf110])()([lim)(xf)](ln)([ln1lim100])()([limxfhxxfhhhhexfhxxfxxFxxFxFx)()(lim)('0hxxxfxF),(ln)()]'([ln)](ln)([lnlim0xfxxfhxxfhxxhxxfxee1)]'([lnxxfx1)]'([ln21)]'([lnxxf'1)(lnCxxfxCexf1)(12/78fydstudio@live.cn1)(limxfxC=1xexf1)(§1.31)(xf)(xg),()(xf0)(xf)(xg(A))]([xfg(B)2)]([xg(C))]([xgf(D))()(xfxg(A)(B)(C)1)(xf0011)(xxxg,(D))()()(xhxfxg)()()(xhxfxg)()(xfxg2)()sinsin(limsinsinxfxtxtxxtkx)sinsinln(sinsinlim)(lnxtxtxxfxtxxxtxtxxtsinsinsinsincoslim)()(sinkxexfxxkx,0x13/78fydstudio@live.cn1)(xf]1,0[0)0(f1)1(f)1,0(1)(f1)()(xxfxg)(xg]1,0[01)0(g01)1(g)1,0(0)(g2)(xf]2,0[3)2()1()0(fff]2,0[1)(f)(xf]2,0[Mfffm)]2()1()0([31]2,0[)]2()1()0([31)(ffff1)(f.11§2.116lim)()1()1(2xnxnneaxexxf)(xf)('xfx)1(limxnne14/78fydstudio@live.cnx0lim)1(xnne.11121)(2xxxbaxbaxxf1x1lim)(lim211xxfxx121)1(baf1ba1x1)1(lim)1('21xfxfx1)1()(lim)1('1xfbaxfx)1(')1('ff212lim)1('1xfxaafx1lim)1('12a11ab.111121)(2xxxxxxf1122)('xxxxf15/78fydstudio@live.cn1qrcos16pqcossinsinsin)cos1(coscoscos)cos1(2yx1sincos2sinsincoscos66226ddxddydxdy)4323(14321xy045343yx)4323(3421xy041341yx2)(xf0x)(8)sin1(3)sin1(xaxxfxf0)(lim0xxax)(xf1x)(xfy)6(,6f)1(')6('),1()6(ffff)6)(1(')1(xffy)1(f)1('f)(xf16/78fydstudio@live.cn)1(2)]sin1(3)sin1([lim0fxfxfx0)1(2f0)1(f8)sin)(sin8(limsin)sin1(3)sin1(lim00xxaxxxxfxfxxtxsin8)1(3)1(lim0ttftft0)1(f)()1()1(lim3)]1()1([lim00tftftftftt)1('4)1('3)1('fff8)1('4f2)1('f)6(20xy0122yx1.)1ln(arctan2tytxxdyd22ttttdtdxdtdydxdy2111222)1(2112)()(2222ttdtdxdtdxdyddxdxdyddxyd2)(xyy122yx''y17/78fydstudio@live.cn0'22yyxyxy'3322221'1''yyxyyyxyyxyyy2.n14323xxxy)(ny(n)1)(4(1213)3(xxxxy14)1)(4(1213xBxAxxx)4()1(1213xBxAx4x4564,645xAA1x151,15xBB])1(1)4(64[5!)1(...])1(51)4(564)2)(1('')1(51)4(5641')1(51)4(564)3(11)()(332211nnnnxxnyxxyxxyxxxy1218/78fydstudio@live.cn2xxycossin4)(ny22)22cos1()22cos1(xxyxx4cos4143)2cos22(412)24cos(4)24cos(4411)(nxnxynnn13)0()(nf0)(nnnxaxf!)0()(nfannnnanf)!()0()()(xf§

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