数学实验二：极限与连续.doc

实验二：极限与连续第一题：数列极限In1= fn_:=Sum1/j3,j,1,n; xn=TableNfn,10,n,30Out1= 1.000000000,1.125000000,1.162037037,1.177662037,1.185662037,1.190291667,1.193207119,1.195160244,1.196531986,1.197531986,1.198283300,1.198862004,1.199317170,1.199681602,1.199977898,1.200222039,1.200425580,1.200597048,1.200742842,1.200867842,1.200975822,1.201069736,1.201151926,1.201224264,1.201288264,1.201345159,1.201395965,1.201441518,1.201482521,1.201519558In2=ListPlotxn,PlotStylePointSize0.02Out2= Graphics第二题：递归数列In3=Clearf; f1=1; fn_:=fn=N(fn-1+3/fn-1)/2,20; fn=Tablefn,n,30Out3= 1,2.0000000000000000000,1.7500000000000000000,1.7321428571428571429,1.7320508100147275405,1.7320508075688772953,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935In4= ListPlotfn,PlotStylePointSize0.02Out4= Graphics第三题：多次自复合In5= PlotSinx,NestSin,x,5,NestSin,x,10,NestSin,x,30,x,-2Pi,2Pi,PlotStyleRGBColor0,0,1,RGBColor1,1,0,RGBColor1,0,0,RGBColor0,1,0Out5= GraphicsIn6= Clearf; fn_:=fn=NestSin,3,n; fn=TableNfn,10,n,30Out6= 0.1411200081,0.1406520768,0.1401887818,0.1397300469,0.1392757977,0.1388259614,0.1383804669,0.1379392448,0.1375022270,0.1370693472,0.1366405402,0.1362157427,0.1357948923,0.1353779282,0.1349647910,0.1345554222,0.1341497650,0.1337477635,0.1333493630,0.1329545100,0.1325631521,0.1321752379,0.1317907173,0.1314095408,0.1310316604,0.1306570285,0.1302855991,0.1299173265,0.1295521663,0.1291900748In7= ListPlotfn,PlotStylePointSize0.02Out7= Graphics第四题：计算极限（1）：In8= Limitx*Sin1/x+(1/x)*Sinx,x0Out8= 1(2)In9= Limit(x2)/E2,xInfinity,Direction-1Out9= (3)In10= Limit(Tanx-Sinx)/x3,x0Out10= (4)In11= Limitxx,x0,Direction-1Out11= 1（5）In12= LimitLogCotx/Logx,x0,Direction-1Out12= -1（6）In13=Limitx2Logx,x0,Direction-1Out13=0（7）In14=Limitx2Logx,x0,Direction-1Out14=（8）In15=Limit(Sinx/x)(1/(1-Cosx),x0Out15=0（9）In16=Limit(Ex-E(-x)-2*x)/(x-Sinx),x0Out16=2第五题：