数学分析数学分析数学分析 (13).pdf

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1、?10.1?1.?Sn(x)=,(i)xnx?e?)1,0(?(ii)x?),1(?Sn(x)=x,xnx?e?),0(?Sn(x)=sinnx,(i)x?),(?(ii)x?,AA?()?0?A?Sn(x)=arctan nx,(i)x?)1,0(?(ii)x?),1(?Sn(x)=221nx?,x?),(?Sn(x)=nx(1?x)n,x?1,0?Sn(x)=nxlnnx,(i)x?)1,0(?(ii)x?)?),1(?Sn(x)=nnxx?1,(i)x?)1,0(?(ii)x?),1(?Sn(x)=(sin x)n,x?,0?Sn(x)=(sin x)n1,(i)x?0,?(ii)x?,

2、?0?3?3?3?Sn(x)=nnx()$%&?1?(i)x?),0(?(ii)x?,0(A()?0?A?Sn(x)=()$%&?xnxn1,(i)x?),0(?,(ii)*?0,?33x?1?(i)?0)(?xS)()(sup),()1,0(xSxSSSdnxn?1?H?0?n?()nSx?(0,1)(ii)?0)(?xS)()(sup),(),1(xSxSSSdnxn?ne?)(0?n?()nSx?(1,)?2?0)(?xS)()(sup),(),0(xSxSSSdnxn?ne1?)(0?n?1?()nSx?(0,)?3?(i)?0)(?xS)()(sup),(),(xSxSSSdnxn?

3、1?H?0?n?()nSx?(,)?(ii)?0)(?xS?An2?)()(sup),(,xSxSSSdnAAxn?nA?)(0?n?()nSx?,A A?4?(i)2)(?xS?)()(sup),()1,0(xSxSSSdnxn?2?H?0?n?()nSx?(0,1)(ii)2)(?xS?)()(sup),(),1(xSxSSSdnxn?narctan2?)(0?n?()nSx?(1,)?5?xxS?)(?nxnxxSxSn11)()(22?)()(sup),(),(xSxSSSdnxn?)(0?n?()nSx?(,)?6?0)(?xS?)1()1(nSnSnnn)11(?H?0?n?()n

4、Sx?0?,1?7?(i)?0)(?xS0)0()0(?SSn?2*?)()(xSxSdxdn0)ln1(1?nxn?)2(.n?nnxSxSSSdnxnln)()(sup),()1,0(?)(0?n?()nSx?(0,1)(ii)?0)(?xS?)2()2(nSnSn2ln2?H?0?n?()nSx?(1,)?8?(i)?0)(?xS?)11()11(nSnSnnnnn)11(1)11(?H?0?n?()nSx?(0,1)(ii)?1)(?xS?)11()11(nSnSn1)11(1)11(?nnnn?H?0?n?()nSx?(1,)?9?2,0021)(?xxxxS?,0?nx?nxn11

5、sin?2?nx?)()(nnnxSxSnn)11(?H?0?n?()nSx?0,?10?(i)?xxxS01,00)(),0(?nx?nnx21sin?3?)()(nnnxSxS121?H?0?n?()nSx?(0,)?(ii)?1)(?xS)()(sup),(xSxSSSdnn?,x?3?33n1sin1?)(0?n?()nSx?,3?3?11?(i)?xexS?)(?)()(nSnSnnne?2?H?0?n?()nSx?(0,)?(ii)?xexS?)(0)0()0(?SSn?n*?)()(xSxSdxdn011?()$%&?xnenx?)()(sup),(,0(xSxSSSdnAxn?

6、nAnAe()$%&?1)(0?n?()nSx?(0,A?12?(i)xxS21)(?)1()1(nSnSnn()$%&?232?H?0?n?()nSx?(0,)?(ii)xxS21)(?Sn(x)=()$%&?xnxn1)(2111xSxxnx?4?*041)1()1(21)()(23?xnxxnxxxSxSdxdn?)()(sup),(),xSxSSSdnxn?3)()(33SSn?333211?()$%&?nn)(0?n?()nSx?,)3?2.?Sn(x)=n(nx?nx2)?S(x)?n 1,0?nlimF10)(xSndx?F?10limnSn(x)dx?Sn(x)?1,00)(?

7、xS?nxn11?)()(nnnxSxS?!#+,-?nnnnn2)11()11(?Sn(x)?1,0?nlimF10)(xSndx?nlimxxxnnnd)(102F?21?SF?10limnn(x)dx0?dx?nlimF10)(xSn?F?10limnSn(x)dx?3.?Sn(x)=221xnx?Sn(x)?),(?)(ddxSxn?),(?nlimxddSn(x)=xdd?nlimSn(x)?x?),(?1?Sn(x)=221xnx?0)(?xS?nxnxxSxSn211)()(22?)(0?n?5?Sn(x)?),(?2?)(xSdxdn22222)1(1xnxn?)(lim)(x

8、Sdxdxnn?E?0001xx?nxn21?)(nnxSdxd2512)(?nxE?H?0?n?)(ddxSxn?),(?3?0?x?xdd?nlimSn(x)?0?)(lim)(xSdxdxnn?E1?0?x?nlimxddSn(x)=xdd?nlimSn(x)?4.?Sn(x)=n1arctan xn?Sn(x)?),0(?nlimxddSn(x)=xdd?nlimSn(x)?Sn(x)=n1arctan?nxnnnxxxS211)(?)(xS?nlimSn(x)0?0)(?xS?)1(21)1(limSSnn?nlimxddSn(x)=xdd?nlimSn(x)?1?x5.?Sn(x)

9、=?a?a?Snxxen?n(x)?1,0?nlimF10)(xSndx=SF?10limnn(x)dx?x?0,1?nlimxddSn(x)=xdd?nlimSn(x)?6?(1)S?)(xS?nlimn(x)?0?)(xSn0)1(?nxennx?nx1?)()(sup),(1,0 xSxSSSdnxn11)1(?ennSn?0),(lim?SSdnn?1?1?Sn(x)?1,0?(2)SF?10limnn(x)dx?F?100)(dxxSF?10)(dxxSnnennn?)11(12?2?.?nlimF10)(xSndx=SF?10limnn(x)dx?(3)xdd?nlimSn(x)x

10、dd?0)(?xS?xddSn(x)?)1(nxennx?)1(limnxenxn?01 1,0(0 xx?0?nlimxddSn(x)=xdd?nlimSn(x)?x?0,1?6.?S(x)?),(baSn(x)=!#+,-?()$%&?)(1xSnxSn?Sn(x)?S(x)?),(ba?S?nlimn(x)?)(xS?0?/B,?)(xSn?*BB?ba,?)(xS?B?0,?)(xS*?ba,?,?0,0?0?/31,?/,xx*?ba,?3?xx,?1?)()(xSxS?!#+,-?!#+,-?B31,1maxN,?Nn?x*BB?ba,?nx1*?ba,7?)()(xSxSn15?

11、)()(xSS?Sn(x)?S(x)?),(ba7.?)(0 xS,0aSn(x)=d t?n=?F?xntS01)(?,2,1?Sn(x)?0?,0a?MxS?)(0,?MxdttSxSx?F001)()(?FF?xxMtdtdttSxS0012)()(!22xM?FF?xnnxnnnxMdtntMdttSxS0101!)!1()()(?!naMnxMnn?0)!(lim?naMnn?Sn(x)?0?,0a8.?S(x)?S(1)=0?x 1,0nS(x)?0,1?S(x)?1,0MxS?)(?,?0)1(?S0,0?0?/31,*1,13?/x?1?)(xSxn?nx?*3?1,0?,N0,Nn?/*3?/1,0 x?Mxn1?1?)(xSxn 8?x 1,0?xnS(x)?0,1?9