數(shù)學實驗二：極限與連續(xù)

1、實驗二：極限與連續(xù)第一題：數(shù)列極限In 1= fn:=Sum1/jA3,j,1, n; xn=TableNf n,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.

2、202267842,1.202275822,1.202269736,1.202251926,1.202224264,1.202288264,1.202245159,1.202295965,1.202241518,1.202282521,1.202219558In 2= ListPlotx n,PlotStylePoi ntSize0.02Out2=Graphics第二題：遞歸數(shù)列In 3= Clearf;f1=1;fn_:=f n=N(f n-1+3/f n-1)/2,20;fn=Tablef n,n, 301.81.61.41.21015202530Out3=In 4=ListPlotfn,

3、PlotStyle Poi ntSize0.02Out4=2卜*Graphics第三題：屢次自復合In 5=PlotSi nx,NestSi n,x,5,NestSi n,x,10,NestSi n,x,30,x,-2Pi,2Pi,PlotStyleRGBColor0,0,1,RGBColor1,1,0,RGBColor1,0,0,RGBColor0,1,0In 6=Clearf;fn_:=f n=NestSi n,3, n; fn=TableNf n,10, n,30Out6=0.1411200081,0.1406520768,0.1401887818,0.1397300469,0.1392

4、757977,0.138825 9614,0.1383804669,0.1379392448,0.1375022270,0.1370693472,0.1366405402,0.136 2157427,0.1357948923,0.1353779282,0.1349647910,0.1345554222,0.1341497650,0.1337477635,0.1333493630,0.1329545100,0.1325631521,0.1321752379,0.1317907173,0.1314095408,0.1310316604,0.1306570285,0.1302855991,0.129

5、9173265,0.129552 1663,0.1291900748In 7= ListPlotfn,PlotStylePoi ntSize0.020.140.1380.1360.13403fiGraphics第四題：計算極限丨：In 8= Limitx*Si n1/x+(1/x)*Si nx,x0Out8=1In 9= Limit(xA2)/EA2,xInfin ity,Directio n-1Out9=In 10= Limit(Ta nx-Si nx)/xA3,x01Out10=2In 11= LimitxAx,xOQirectio n-1Out11= 15OQirectio n -1In 12= LimitLogCotx/Logx,xOut12= -16In 13= LimitxA2Log x,x0,Directio n-1Out13= 07In 14= LimitxA2Log x,x0,Directio n-11Out14= 38In 15= Limit(Si n x/x)A(1心-Cos x),x0Out15= 09In 16= Limit(EAx-EA(-x)-2*x)/(x-Si nx),x0Out16= 2第五題：討論極限-121.2In 17= PlotEvaluateTable