数学分析课本(华师大三版)-习题及答案part-inew

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1、PartILimits1.Supposelim((xaxb+)(+)+cx

2、

3、)exists.Findtheconstantcandtherelationx®¥betweenaandb.22.Supposelim(x+2x-ax)exists.Findtheconstantaandthislimit.x®-¥23.Findtheasymptoticlineofy=4x+2x+3.2xsinx-14.Supposefx()=.Findlimsup()fxandliminffx().2x-sinxx®+¥x®+¥nn5.Suppos

4、e∑ak=0.Findthelimitlim∑aksinxk+.x®+¥k=1k=1nn6.Suppose∑ak=0.Findthelimitlim∑akcosxk+.x®+¥k=1k=1n22n7.Findthelimitlim(1)-n[cosp1+n--(1)].n®¥n28.Findthelimitlim(1)-nsinp1+n.n®¥9.Findthefollowinglimits:xxx1an2a+b+c(1)lim(cos);(2)lim()(,,xabc>0).n®¥nx®03xxx10.Findthelimit

5、limcoscosLcos.nn®¥242nn+lnn11.Findthelimitlim()lnn.n®¥n-lnnaa12.Findthelimitlim[(n+1)-n](0

6、.n®¥(2)!!n12x+115.(1)Supposefx()=.Discusstheexistenceofthelimitlim()fx;1x®02x-1xsintsint-sinx(2)Supposefx(=lim().Determinethetypesofitsdiscontinuouspoints.sinxt®xxb16.Findthelimitlim[](ab¹0).x®0ax2217.(1)Assumex>a>0,x=x-2ax+2a.Findthelimitlima;1n+1nnnn®¥1(2)Assumea=>

7、c0,a=+c.Findthelimitlima;1n+1nan®¥n2abnn(3)Assume00,x=.Findthelimitlimx;1n+1n3+xn®¥n2cca(2)Assumec>0,a=,a=+.Findthelimitlima;1n+1n222n®¥n1(3)Assumefx()=x+xc,Î(,1),fc()1=.Findt

8、helimitlimc.nnnn2n®¥a+xn19.Assumex>0,a>0,x=.Discusswhetherthesequence{}xisconvergent1n+1n1+xnornot.Suppose{}xisconvergent.Finditslimit.nu+vnn20.Letu=av,=b(0<

9、nt.k=2klnkn122.Provethatthesequence{∑-ln}nisconvergent.k=1kxxn+1n23.Assumex>0,=ln(1+).Findthelimitlimx.1nn+1nn®¥24.Assume00,a=a+.Provethatlim=2.1n+1nan®¥nn27.Suppos

10、ethat{}aand{}barenaturalnumbersequences.Assumenn2ana=b=>10,a+b2=(a+b2).Findthelimitlim.11nnn-1n-1n®¥bpn28.Assumep>0,q>0,p=p+3,qq=p+