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Please answer this:1+4 =



Original Message (ID '268164') By Bill Simpson:
In Response To 'Re: Re: Re: Re: Solve equation(s) with a List a...' --------- Carefully use exact rational numbers to maintain precision for this example. In[1]:= mag=49/30*10^-14; w=5/1000; d:=148*10^(-9); mu0:=4*Pi*10^(-7); B:=5/10000; Table[{x,N[(w*d*B+mu0*mag)/(2*w*B)-x*Tanh[d/(2*x)],30]},{x,1,20}] Out[6]= { {1, 4.105014535765329831590891486602017102673418`30.*^-15}, {2, 4.105014434459329831591168862430017102027881`30.*^-15}, {3, 4.105014415698959461220813331095712575269563`30.*^-15}, {4, 4.105014409132829831591186198419267102017795`30.*^-15}, {5, 4.105014406093649831591186880763803982017677`30.*^-15}, {6, 4.105014404442737238998594533266428624651394`30.*^-15}, {7, 4.105014403447289015264656618680184532255041`30.*^-15}, {8, 4.105014402801204831591187281918595227017637`30.*^-15}, {9, 4.105014402358251642290775786423252482803085`30.*^-15}, {10, 4.105014402041409831591187324565128782017635`30.*^-15}, {11, 4.105014401806982724153170805018112177490622`30.*^-15}, {12, 4.105014401628681683443039191735431711071133`30.*^-15}, {13, 4.105014401489921547567518704739483997434462`30.*^-15}, {14, 4.105014401379819627509554693388984199060534`30.*^-15}, {15, 4.105014401290995016776372533492771672552614`30.*^-15}, {16, 4.105014401218298581591187349637303234830135`30.*^-15}, {17, 4.105014401158049554774578354069658341945318`30.*^-15}, {18, 4.105014401107560284266084470675017152822898`30.*^-15}, {19, 4.105014401064831216632738598418981551338926`30.*^-15}, {20, 4.105014401028349831591187352302711582017635`30.*^-15}} You can see how slowly this is going to converge on zero as x increases. If you introduce a decimal point ANYWHERE in this you should see the results are immediately compromised by $MachinePrecision approximate calculations. Try it and see. Spot the single difference in the code. In[7]:= mag=49/30*10^-14; w=5/1000; d:=148*10^(-9); mu0:=4*Pi*10^(-7); B:=5/10000.; Table[{x,N[(w*d*B+mu0*mag)/(2*w*B)-x*Tanh[d/(2*x)],30]},{x,1,20}] Out[12]= { {1, 4.105014524035853`*^-15}, {2, 4.105014431391624`*^-15}, {3, 4.105014418156734`*^-15}, {4, 4.1050144049218444`*^-15}, {5, 4.1050144049218444`*^-15}, {6, 4.105014391686955`*^-15}, {7, 4.105014391686955`*^-15}, {8, 4.105014391686955`*^-15}, {9, 4.105014391686955`*^-15}, {10, 4.105014391686955`*^-15}, {11, 4.105014391686955`*^-15}, {12, 4.105014391686955`*^-15}, {13, 4.105014391686955`*^-15}, {14, 4.105014391686955`*^-15}, {15, 4.105014391686955`*^-15}, {16, 4.105014391686955`*^-15}, {17, 4.105014391686955`*^-15}, {18, 4.105014391686955`*^-15}, {19, 4.105014391686955`*^-15}, {20, 4.105014391686955`*^-15}} Mathematica floating point calculations are not FORTRAN floating point calculations.