doc plot edit pol left = 0; right = 4; n=10; x = linspace( left, right, n ); y = pol( x ); {Error using ^ Inputs must be a scalar and a square matrix. To compute elementwise POWER, use POWER (.^) instead. Error in pol (line 3) y = .5*x^3 - x^2 + 3*x -.5; } y = pol( x ); plot( x, y ) close all; plot( x, y, 'g*-') whitebg('black') axis([0 3 -1 1]) hold on; plot( x, y, 'ro-') axis([0 3 -3 4]) y = pol( x ); plot( x, y, 'ro-') axis([0 3 -10 10]) ezplot( sin ) {Error using sin Not enough input arguments. } ezplot( @sin ) hold off ezplot( @sin ) ezplot( @sin, [0 1] ) edit pol3 edit myplot3 myplot3 M = [ linspace( 2, 4, 4 ); linspace( 1, 5, 4 ); ] M = 2.0000 2.6667 3.3333 4.0000 1.0000 2.3333 3.6667 5.0000 reshape( M, 4, 4 ) {Error using reshape To RESHAPE the number of elements must not change. } reshape( M, 8, 1 ) ans = 2.0000 1.0000 2.6667 2.3333 3.3333 3.6667 4.0000 5.0000 M = [ linspace( 2, 4, 4 ); linspace( 5, 1, -4 ); ] M = 2.0000 2.6667 3.3333 4.0000 M = [ 2:.5:4; 5:-1:1 ] M = 2.0000 2.5000 3.0000 3.5000 4.0000 5.0000 4.0000 3.0000 2.0000 1.0000 M = [ 2:.5:4; 5.3:-1:1.3 ] M = 2.0000 2.5000 3.0000 3.5000 4.0000 5.3000 4.3000 3.3000 2.3000 1.3000 reshape( M, 10, 1 ) ans = 2.0000 5.3000 2.5000 4.3000 3.0000 3.3000 3.5000 2.3000 4.0000 1.3000 x = reshape( M, 10, 1 ) x = 2.0000 5.3000 2.5000 4.3000 3.0000 3.3000 3.5000 2.3000 4.0000 1.3000 y = pol( x ); plot( x, y, 'b+-' ) x = sort(x); y = pol( x ); close all; plot( x, y, 'b+-' ) plot( x, y, 'w+-' ) myplot {Undefined function or variable 'myplot'. } myplot3 myplot3 myplot3 myplot3 z = -4 z = -3.7895 z = -3.5789 z = -3.3684 z = -3.1579 z = -2.9474 z = -2.7368 z = -2.5263 z = -2.3158 z = -2.1053 z = -1.8947 z = -1.6842 z = -1.4737 z = -1.2632 z = -1.0526 z = -0.8421 z = -0.6316 z = -0.4211 z = -0.2105 z = 0 z = -5.2188 z = -4.8404 z = -4.4805 z = -4.1394 z = -3.8169 z = -3.5130 z = -3.2279 z = -2.9614 z = -2.7135 z = -2.4843 z = -2.2738 z = -2.0819 z = -1.9087 z = -1.7542 z = -1.6183 z = -1.5011 z = -1.4025 z = -1.3226 z = -1.2614 z = -1.2188 z = -6.3490 z = -5.8026 z = -5.2935 z = -4.8217 z = -4.3872 z = -3.9901 z = -3.6303 z = -3.3078 z = -3.0226 z = -2.7747 z = -2.5642 z = -2.3910 z = -2.2551 z = -2.1566 z = -2.0953 z = -2.0714 z = -2.0849 z = -2.1356 z = -2.2236 z = -2.3490 z = -7.3906 z = -6.6762 z = -6.0178 z = -5.4154 z = -4.8689 z = -4.3785 z = -3.9440 z = -3.5655 z = -3.2430 z = -2.9765 z = -2.7660 z = -2.6115 z = -2.5129 z = -2.4703 z = -2.4837 z = -2.5531 z = -2.6785 z = -2.8599 z = -3.0972 z = -3.3906 z = -8.3435 z = -7.4611 z = -6.6534 z = -5.9204 z = -5.2620 z = -4.6782 z = -4.1691 z = -3.7347 z = -3.3748 z = -3.0897 z = -2.8791 z = -2.7433 z = -2.6820 z = -2.6954 z = -2.7835 z = -2.9462 z = -3.1836 z = -3.4956 z = -3.8822 z = -4.3435 z = -9.2078 z = -8.1575 z = -7.2005 z = -6.3368 z = -5.5664 z = -4.8893 z = -4.3056 z = -3.8151 z = -3.4180 z = -3.1142 z = -2.9036 z = -2.7864 z = -2.7625 z = -2.8319 z = -2.9946 z = -3.2506 z = -3.5999 z = -4.0426 z = -4.5785 z = -5.2078 z = -9.9834 z = -8.7651 z = -7.6588 z = -6.6645 z = -5.7822 z = -5.0118 z = -4.3534 z = -3.8070 z = -3.3725 z = -3.0500 z = -2.8395 z = -2.7409 z = -2.7543 z = -2.8797 z = -3.1171 z = -3.4664 z = -3.9277 z = -4.5009 z = -5.1862 z = -5.9834 z = -10.6704 z = -9.2842 z = -8.0286 z = -6.9036 z = -5.9093 z = -5.0456 z = -4.3126 z = -3.7102 z = -3.2384 z = -2.8972 z = -2.6867 z = -2.6068 z = -2.6575 z = -2.8389 z = -3.1509 z = -3.5935 z = -4.1668 z = -4.8707 z = -5.7052 z = -6.6704 z = -11.2687 z = -9.7145 z = -8.3097 z = -7.0541 z = -5.9478 z = -4.9908 z = -4.1831 z = -3.5247 z = -3.0156 z = -2.6558 z = -2.4453 z = -2.3840 z = -2.4721 z = -2.7094 z = -3.0961 z = -3.6320 z = -4.3172 z = -5.1518 z = -6.1356 z = -7.2687 z = -11.7784 z = -10.0563 z = -8.5021 z = -7.1159 z = -5.8977 z = -4.8474 z = -3.9650 z = -3.2506 z = -2.7042 z = -2.3257 z = -2.1152 z = -2.0726 z = -2.1980 z = -2.4913 z = -2.9526 z = -3.5819 z = -4.3791 z = -5.3442 z = -6.4773 z = -7.7784 z = -12.1994 z = -10.3094 z = -8.6059 z = -7.0891 z = -5.7589 z = -4.6153 z = -3.6583 z = -2.8879 z = -2.3041 z = -1.9070 z = -1.6965 z = -1.6725 z = -1.8353 z = -2.1846 z = -2.7205 z = -3.4431 z = -4.3522 z = -5.4480 z = -6.7304 z = -8.1994 z = -12.5319 z = -10.4738 z = -8.6211 z = -6.9736 z = -5.5314 z = -4.2945 z = -3.2629 z = -2.4365 z = -1.8154 z = -1.3996 z = -1.1891 z = -1.1838 z = -1.3839 z = -1.7892 z = -2.3998 z = -3.2156 z = -4.2368 z = -5.4632 z = -6.8949 z = -8.5319 z = -12.7756 z = -10.5496 z = -8.5476 z = -6.7695 z = -5.2153 z = -3.8851 z = -2.7788 z = -1.8965 z = -1.2381 z = -0.8036 z = -0.5931 z = -0.6065 z = -0.8439 z = -1.3051 z = -1.9904 z = -2.8995 z = -4.0327 z = -5.3897 z = -6.9707 z = -8.7756 z = -12.9307 z = -10.5368 z = -8.3855 z = -6.4767 z = -4.8106 z = -3.3871 z = -2.2062 z = -1.2678 z = -0.5721 z = -0.1190 z = 0.0916 z = 0.0595 z = -0.2152 z = -0.7325 z = -1.4923 z = -2.4948 z = -3.7399 z = -5.2276 z = -6.9579 z = -8.9307 z = -12.9972 z = -10.4353 z = -8.1347 z = -6.0953 z = -4.3172 z = -2.8004 z = -1.5448 z = -0.5505 z = 0.1825 z = 0.6543 z = 0.8648 z = 0.8141 z = 0.5021 z = -0.0711 z = -0.9057 z = -2.0015 z = -3.3585 z = -4.9768 z = -6.8564 z = -8.9972 z = -12.9751 z = -10.2452 z = -7.7953 z = -5.6253 z = -3.7352 z = -2.1251 z = -0.7949 z = 0.2554 z = 1.0258 z = 1.5163 z = 1.7268 z = 1.6574 z = 1.3081 z = 0.6788 z = -0.2304 z = -1.4194 z = -2.8885 z = -4.6374 z = -6.6663 z = -8.9751 z = -12.8643 z = -9.9665 z = -7.3673 z = -5.0666 z = -3.0646 z = -1.3611 z = 0.0437 z = 1.1500 z = 1.9577 z = 2.4668 z = 2.6774 z = 2.5893 z = 2.2027 z = 1.5174 z = 0.5336 z = -0.7488 z = -2.3298 z = -4.2094 z = -6.3875 z = -8.8643 z = -12.6648 z = -9.5991 z = -6.8506 z = -4.4193 z = -2.3053 z = -0.5085 z = 0.9710 z = 2.1333 z = 2.9783 z = 3.5061 z = 3.7166 z = 3.6099 z = 3.1859 z = 2.4447 z = 1.3862 z = 0.0105 z = -1.6825 z = -3.6927 z = -6.0201 z = -8.6648 z = -12.3767 z = -9.1430 z = -6.2452 z = -3.6833 z = -1.4574 z = 0.4327 z = 1.9869 z = 3.2051 z = 4.0875 z = 4.6339 z = 4.8444 z = 4.7191 z = 4.2578 z = 3.4606 z = 2.3275 z = 0.8584 z = -0.9465 z = -3.0873 z = -5.5641 z = -8.3767 z = -12 z = -8.5983 z = -5.5512 z = -2.8587 z = -0.5208 z = 1.4626 z = 3.0914 z = 4.3657 z = 5.2853 z = 5.8504 z = 6.0609 z = 5.9169 z = 5.4183 z = 4.5651 z = 3.3573 z = 1.7950 z = -0.1219 z = -2.3934 z = -5.0194 z = -8 myplot3 ezplot( @pol ) close all; ezplot( @pol ) sqr = @(x) x.^2 sqr = @(x)x.^2 sqr( 4 ) ans = 16 ezplot( sqr ) edit fun1 fun1( 0, 1 ) ans = -1 function z = fun1( t, y ) | {Error: Function definitions are not permitted in this context. } n = 10; t = linspace( 0, 3, n ); t(1) = 1; n = 2; a = 0; b = 3; h = (b-a)/n; t = linspace( 0, 3, n ) t = 0 3 n = 2; a = 0; b = 3; h = (b-a)/n; t = linspace( 0, 3, n+1 ) t = 0 1.5000 3.0000 n = 2; a = 0; b = 3; h = (b-a)/n; t = linspace( 0, 3, n+1 ); h h = 1.5000 n = 2; a = 0; b = 3; h = (b-a)/n; t = linspace( 0, 3, n+1 ); y(1) = 1; for i = 2:n, y(i) = y(i-1) + h*fun1( t(i-1), y(i-1) ); end plot( t, y ) {Error using plot Vectors must be the same length. } length(t) ans = 3 length(y) ans = 400 clear('y') for i = 2:n, y(i) = y(i-1) + h*fun1( t(i-1), y(i-1) ); end {Undefined function or variable 'y'. } y(1) = 1; for i = 2:n, y(i) = y(i-1) + h*fun1( t(i-1), y(i-1) ); end plot( t, y ) {Error using plot Vectors must be the same length. } whos('y') Name Size Bytes Class Attributes y 1x2 16 double n = 10; a = 0; b = 3; h = (b-a)/n; t = linspace( 0, 3, n+1 ); n = 10; a = 0; b = 3; h = (b-a)/n; t = linspace( 0, 3, n+1 ); y(1) = 1; for i = 2:n, y(i) = y(i-1) + h*fun1( t(i-1), y(i-1) ); end whos('t') Name Size Bytes Class Attributes t 1x11 88 double whos('n') Name Size Bytes Class Attributes n 1x1 8 double whos('y') Name Size Bytes Class Attributes y 1x10 80 double for i = 2:n+1, y(i) = y(i-1) + h*fun1( t(i-1), y(i-1) ); end plot( t, y ) n = 100; a = 0; b = 3; h = (b-a)/n; t = linspace( 0, 3, n+1 ); y(1) = 1; for i = 2:n+1, y(i) = y(i-1) + h*fun1( t(i-1), y(i-1) ); end close all; plot( t, y ) sol = @(t) exp(-t) * cos(5*t) sol = @(t)exp(-t)*cos(5*t) sol( t ) {Error using * Inner matrix dimensions must agree. Error in @(t)exp(-t)*cos(5*t) } sol(0) ans = 1 sol(3) ans = -0.0378 format long sol(3) ans = -0.037822634055742 y(end) ans = -0.037896264491903 sol( y ) {Error using * Inner matrix dimensions must agree. Error in @(t)exp(-t)*cos(5*t) } sol = @(t) exp(-t) .* cos(5*t) sol = @(t)exp(-t).*cos(5*t) sol( y ) ans = Columns 1 through 4 0.104353486269682 0.052001516413462 -0.046423525102459 -0.191030853468242 Columns 5 through 8 -0.361377449593051 -0.504032992157408 -0.537622440228157 -0.387226981102216 Columns 9 through 12 -0.038987711551221 0.421975830440460 0.830344137655809 1.017721513498643 Columns 13 through 16 0.899292031348634 0.510123888024507 -0.027661349648993 -0.574261533046739 Columns 17 through 20 -1.029726606920796 -1.353858095511375 -1.553474278934048 -1.656562898834221 Columns 21 through 24 -1.689735241380445 -1.665931454361633 -1.582408263242207 -1.426428437523448 Columns 25 through 28 -1.185543840488392 -0.858835948927268 -0.464804531771425 -0.042059152862089 Columns 29 through 32 0.358444824922948 0.686932591735934 0.908416275033252 1.010738777254311 Columns 33 through 36 1.004475975275649 0.916117921078458 0.778463394847591 0.622191745495058 Columns 37 through 40 0.470849006204548 0.339452833987461 0.235629149993288 0.161869658486503 Columns 41 through 44 0.117812293338932 0.101952764834923 0.112611251310003 0.148220802411667 Columns 45 through 48 0.207110714150592 0.286996972213651 0.384408073239325 0.494276005816313 Columns 49 through 52 0.609890557322316 0.723329972289200 0.826344336739195 0.911515643039954 Columns 53 through 56 0.973408550181390 1.009409179037865 1.020038510656838 1.008686325749404 Columns 57 through 60 0.980875146776477 0.943269834286068 0.902669196272626 0.865163303433793 Columns 61 through 64 0.835551925033782 0.817035896080053 0.811139648288980 0.817804782837368 Columns 65 through 68 0.835601530687178 0.862021528679367 0.893828214366321 0.927443872421876 Columns 69 through 72 0.959345984648710 0.986436221473972 1.006340686432574 1.017605045073945 Columns 73 through 76 1.019763508905773 1.013282308949428 0.999399745750037 0.979899967869152 Columns 77 through 80 0.956862858114222 0.932427936689940 0.908599041963962 0.887102981764760 Columns 81 through 84 0.869303195938022 0.856161102756745 0.848233883355368 0.845697322251849 Columns 85 through 88 0.848384593224234 0.855835060955732 0.867350036155484 0.882054214350802 Columns 89 through 92 0.898961981318915 0.917047048465768 0.935312467396216 0.952856595779651 Columns 93 through 96 0.968929657112838 0.982975584438421 0.994655000747745 1.003847287408740 Columns 97 through 100 1.010632295432128 1.015254815173786 1.018076931939366 1.019524520608433 Column 101 1.020034264218266 exact = sol( y ); exact = sol( t ); max( abs(exact - y)./exact ) ans = 1.276252495531087 exact exact = Columns 1 through 4 1.000000000000000 0.959548476284976 0.899702023097390 0.822946687527225 Columns 5 through 8 0.732007024013916 0.629770445701126 0.519212289612792 0.403323252671911 Columns 9 through 12 0.285040705344865 0.167185214049475 0.052403407875472 -0.056881884773390 Columns 13 through 16 -0.158513522701115 -0.250633476673835 -0.331707527523356 -0.400541185954253 Columns 17 through 20 -0.456286984399144 -0.498443478086242 -0.526846460780452 -0.541653047698029 Columns 21 through 24 -0.543319401780100 -0.532572978398499 -0.510380236860953 -0.477910814610749 Columns 25 through 28 -0.436499182201738 -0.387604794945871 -0.332771732045996 -0.273588767943680 Columns 29 through 32 -0.211650755797764 -0.148522122024247 -0.085703176449320 -0.024599837774347 Columns 33 through 36 0.033502738289018 0.087462257701009 0.136296861520342 0.179198039258522 Columns 37 through 40 0.215538860828837 0.244877613115507 0.266957026344823 0.281699364624537 Columns 41 through 44 0.289197732789170 0.289704016949230 0.283613928140726 0.271449656801585 Columns 45 through 48 0.253840670390634 0.231503197555631 0.205218940384062 0.175813542231448 Columns 49 through 52 0.144135313443450 0.111034682189645 0.077344793981631 0.043863632743293 Columns 53 through 56 0.011337980097020 -0.019550530579308 -0.048197071193733 -0.074082856138344 Columns 57 through 60 -0.096781891179881 -0.115965225969549 -0.131402759155826 -0.142962697708025 Columns 61 through 64 -0.150608819314580 -0.154395727849825 -0.154462326330949 -0.151023759122699 Columns 65 through 68 -0.144362095184625 -0.134816036865100 -0.122769944266577 -0.108642463831234 Columns 69 through 72 -0.092875041957835 -0.075920590713622 -0.058232553704785 -0.040254596652364 Columns 73 through 76 -0.022411119983277 -0.005098760622651 0.011320981985338 0.026527893947810 Columns 77 through 80 0.040247901114203 0.052256594704873 0.062381425829242 0.070502596666932 Columns 81 through 84 0.076552704011380 0.080515215912718 0.082421883905718 0.082349211468062 Columns 85 through 88 0.080414113721293 0.076768913856897 0.071595828332551 0.065101095617511 Columns 89 through 92 0.057508902332347 0.049055256261602 0.039981948217213 0.030530734448400 Columns 93 through 96 0.020937858625074 0.011429017792938 0.002214860554999 -0.006512911469627 Columns 97 through 100 -0.014584785671251 -0.021855988703115 -0.028208327440439 -0.033551320221031 Column 101 -0.037822634055742 max( abs(exact - y) ) ans = 0.046678059686664 max( abs(exact - y)./exact ) ans = 1.276252495531087 max( (exact - y)./exact ) ans = 1.141713261727473 (y(end) - exact(end))/exact(end) ans = 0.001946729465011 n = 1000; a = 0; b = 3; h = (b-a)/n; t = linspace( 0, 3, n+1 ); y(1) = 1; for i = 2:n+1, y(i) = y(i-1) + h*fun1( t(i-1), y(i-1) ); end exact = sol( t ); (y(end) - exact(end))/exact(end) ans = 7.272437623209290e-04 n = 10; a = 0; b = 3; h = (b-a)/n; t = linspace( 0, 3, n+1 ); y(1) = 1; for i = 2:n+1, y(i) = y(i-1) + h*fun1( t(i-1), y(i-1) ); end exact = sol( t ); (y(end) - exact(end))/exact(end) ans = 7.272437623209290e-04 clear('t') clear all n = 10; a = 0; b = 3; h = (b-a)/n; t = linspace( 0, 3, n+1 ); y(1) = 1; for i = 2:n+1, y(i) = y(i-1) + h*fun1( t(i-1), y(i-1) ); end exact = sol( t ); (y(end) - exact(end))/exact(end) {Undefined function or variable 'sol'. } sol = @(t) exp(-t) .* cos(5*t) sol = @(t)exp(-t).*cos(5*t) exact = sol( t ); (y(end) - exact(end))/exact(end) ans = -0.602534223273937 n = 1000; a = 0; b = 3; h = (b-a)/n; t = linspace( 0, 3, n+1 ); y(1) = 1; for i = 2:n+1, y(i) = y(i-1) + h*fun1( t(i-1), y(i-1) ); end exact = sol( t ); (y(end) - exact(end))/exact(end) ans = 7.272437623209290e-04 n = 10000; a = 0; b = 3; h = (b-a)/n; t = linspace( 0, 3, n+1 ); y(1) = 1; for i = 2:n+1, y(i) = y(i-1) + h*fun1( t(i-1), y(i-1) ); end exact = sol( t ); (y(end) - exact(end))/exact(end) ans = 7.799831062937499e-05 n = 100000; a = 0; b = 3; h = (b-a)/n; t = linspace( 0, 3, n+1 ); y(1) = 1; for i = 2:n+1, y(i) = y(i-1) + h*fun1( t(i-1), y(i-1) ); end exact = sol( t ); (y(end) - exact(end))/exact(end) ans = 7.852521557373846e-06 n = 1000000; a = 0; b = 3; h = (b-a)/n; t = linspace( 0, 3, n+1 ); y(1) = 1; for i = 2:n+1, y(i) = y(i-1) + h*fun1( t(i-1), y(i-1) ); end exact = sol( t ); (y(end) - exact(end))/exact(end) ans = 7.857789108854612e-07 max(abs(y - exact)) ans = 4.681017783281227e-06 edit myeuler myeuler( @fun1, 0, 3, 10, 1 ) ans = Columns 1 through 4 1.000000000000000 0.700000000000000 -0.618443691672424 -0.549083037934104 Columns 5 through 8 0.211793004434057 0.274492599267961 -0.121799308067884 -0.187443606786559 Columns 9 through 11 0.030376076322544 0.094278448793071 -0.015033202622791 myeuler( @fun1, 0, 3, 100, 1 ); y = myeuler( @fun1, 0, 3, 100, 1 ); y(end) ans = -0.037896264491903 y = myeuler( @fun1, 0, 3, 100, 1 ); just DISPlays a string it is just like in C: y(y = myeuler( @fun1, 0, 3, 100, 1 ); just DISPlays a string it is just like in C: y( y = myeuler( @fun1, 0, 3, 100, 1 ); just DISPlays a string it is just like in C! y(y = myeuler( @fun1, 0, 3, 100, 1 ); just DISPlays a string it is just like in C! y(101)= -0.037896y = myeuler( @fun1, 0, 3, 100, 1 ); just DISPlays a string it is just like in C! y(101)= -0.037896264492 doc fpirntf edit sqrts.m edit sqsqrt edit sqrtsq sqrts( 2, 7 ) 7, 1.999999999999971, 2.000000000000000 sqrts( 2, 8 ) 7, 1.999999999999971, 2.000000000000000 8, 2.000000000000024, 2.000000000000000 sqrts( 2, 9 ) 7, 1.999999999999971, 2.000000000000000 8, 2.000000000000024, 2.000000000000000 9, 2.000000000000024, 2.000000000000000 sqrts( 2, 10 ) 7, 1.999999999999971, 2.000000000000000 8, 2.000000000000024, 2.000000000000000 9, 2.000000000000024, 2.000000000000000 10, 2.000000000000024, Inf clc sqrts( 2.2, 10 ) 7, 2.200000000000012, 2.200000000000000 8, 2.200000000000079, 2.200000000000000 9, 2.200000000000079, 2.200000000000000 10, 2.200000000000079, Inf sqrts( 3.2, 10 ) 7, 3.199999999999936, 3.200000000000000 8, 3.199999999999936, 3.200000000000000 9, 3.200000000000114, 3.200000000000000 10, 3.199999999999755, Inf sqrts( .2, 10 ) 7, 0.200000000000002, 0.200000000000000 8, 0.200000000000002, 0.200000000000000 9, 0.200000000000002, 0.000000000000000 10, 0.199999999999990, 0.000000000000000 clc sqrts( 1.2, 12 ) 7, 1.199999999999998, 1.200000000000000 8, 1.199999999999962, 1.200000000000000 9, 1.199999999999896, 1.200000000000000 10, 1.200000000000032, 1.200000000000000 11, 1.200000000000305, 1.200000000000000 12, 1.199999999999761, Inf sqrts( 2.2, 12 ) 7, 2.200000000000012, 2.200000000000000 8, 2.200000000000079, 2.200000000000000 9, 2.200000000000079, 2.200000000000000 10, 2.200000000000079, Inf 11, 2.200000000000079, Inf 12, 2.200000000000079, Inf sqrts( 0.7, 12 ) 7, 0.700000000000003, 0.700000000000000 8, 0.699999999999993, 0.700000000000000 9, 0.699999999999993, 0.700000000000000 10, 0.699999999999953, 0.700000000000000 11, 0.699999999999953, 0.699999999973900 12, 0.699999999999832, 0.000000000000000 sqrts( 0.7, 15 ) 7, 0.700000000000003, 0.700000000000000 8, 0.699999999999993, 0.700000000000000 9, 0.699999999999993, 0.700000000000000 10, 0.699999999999953, 0.700000000000000 11, 0.699999999999953, 0.699999999973900 12, 0.699999999999832, 0.000000000000000 13, 0.699999999999513, 0.000000000000000 14, 0.699999999999513, 0.000000000000000 15, 0.699999999998245, 0.000000000000000 sqrts( 0.7, 20 ) 7, 0.700000000000003, 0.700000000000000 8, 0.699999999999993, 0.700000000000000 9, 0.699999999999993, 0.700000000000000 10, 0.699999999999953, 0.700000000000000 11, 0.699999999999953, 0.699999999973900 12, 0.699999999999832, 0.000000000000000 13, 0.699999999999513, 0.000000000000000 14, 0.699999999999513, 0.000000000000000 15, 0.699999999998245, 0.000000000000000 16, 0.700000000000752, 0.000000000000000 17, 0.700000000000752, 0.000000000000000 18, 0.700000000000752, 0.000000000000000 19, 0.700000000000752, 0.000000000000000 20, 0.700000000000752, 0.000000000000000 sqrts( 0.5, 20 ) 7, 0.499999999999999, 0.500000000000000 8, 0.499999999999999, 0.500000000000000 9, 0.499999999999999, 0.500000000000000 10, 0.499999999999999, 0.500000000000000 11, 0.499999999999999, 0.000000000000000 12, 0.500000000000114, 0.000000000000000 13, 0.500000000000114, 0.000000000000000 14, 0.500000000000571, 0.000000000000000 15, 0.500000000001479, 0.000000000000000 16, 0.500000000001479, 0.000000000000000 17, 0.500000000001479, 0.000000000000000 18, 0.500000000008752, 0.000000000000000 19, 0.500000000008752, 0.000000000000000 20, 0.500000000037885, 0.000000000000000 sqrts( 0.1, 20 ) 7, 0.099999999999999, 0.100000000000000 8, 0.099999999999999, 0.100000000000000 9, 0.100000000000002, 0.000000000000000 10, 0.100000000000002, 0.000000000000000 11, 0.100000000000002, 0.000000000000000 12, 0.100000000000002, 0.000000000000000 13, 0.100000000000002, 0.000000000000000 14, 0.100000000000095, 0.000000000000000 15, 0.100000000000095, 0.000000000000000 16, 0.100000000000460, 0.000000000000000 17, 0.100000000000460, 0.000000000000000 18, 0.100000000000460, 0.000000000000000 19, 0.100000000003375, 0.000000000000000 20, 0.099999999997554, 0.000000000000000 sqrts( 4.1, 20 ) 7, 4.099999999999977, 4.100000000000000 8, 4.100000000000105, 4.100000000000000 9, 4.100000000000337, Inf 10, 4.099999999999857, Inf 11, 4.100000000000778, Inf 12, 4.100000000000778, Inf 13, 4.100000000000778, Inf 14, 4.100000000008135, Inf 15, 4.099999999993023, Inf 16, 4.099999999993023, Inf 17, 4.100000000053106, Inf 18, 4.099999999933824, Inf 19, 4.100000000172273, Inf 20, 4.100000000648643, Inf diary