# Code snips for exact/error reports 2.4-#5

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# Making multiple curves on one plot
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  Exact:=x->2+x-exp(x);               # An exact solution for #5
  plot({Exact(x),[Dots]},x=0..1/2);   # plot exact and approx solutions


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# How to create a Dots table for the exact solution
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Exact:= x -> 2+x-exp(x):
ExactDots:=seq([Dots[j][1],Exact(Dots[j][1])],j=1..11);


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# How to define and print percentage error:
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  Perr:=(exact,approx)->evalf(100*abs(exact-approx)/abs(exact));
  ExactVal:=ExactDots[11][2]:   # Pick off exact y-value for x=0.5
  ApproxVal:=Dots[11][2]:       # Get Euler approx y-value for x=0.5
  Perr(ExactVal),ApproxVal);    # print percent relative error


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# How to create a Dots table for percentage error
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Perr:=(exact,approx)->evalf(100*abs(exact-approx)/abs(exact));
PerrDots:=seq([Dots[j][1],Perr(ExactDots[j][2],Dots[j][2])],j=1..11);


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# Printing results and tables
# Make tables with a pencil, it saves time. 
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# To extract and print items 1,101,201,1001 from a list:
Dots1:=Dots[1],Dots[101],Dots[201],Dots[1001];

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