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A201937
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Decimal expansion of the greatest negative number x satisfying 2*x^2=e^(-x).
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3
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1, 4, 8, 7, 9, 6, 2, 0, 6, 5, 4, 9, 8, 1, 7, 7, 1, 5, 6, 2, 5, 4, 3, 7, 0, 1, 2, 0, 9, 3, 2, 6, 3, 2, 5, 6, 3, 7, 2, 6, 4, 8, 4, 2, 4, 3, 7, 8, 0, 2, 1, 0, 6, 8, 4, 6, 2, 3, 6, 9, 6, 8, 9, 7, 7, 2, 6, 8, 6, 8, 0, 9, 4, 4, 6, 2, 7, 6, 8, 7, 4, 4, 2, 2, 8, 9, 2, 0, 8, 3, 0, 1, 2, 0, 9, 0, 1, 8, 8
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OFFSET
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1,2
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COMMENTS
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See A201936 for a guide to related sequences. The Mathematica program includes a graph.
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LINKS
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EXAMPLE
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least x: -2.617866613066812769178978059143202...
greatest negative x: -1.487962065498177156254...
greatest x: 0.5398352769028200492118039083633...
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MATHEMATICA
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a = 2; b = 0; c = 0;
f[x_] := a*x^2 + b*x + c; g[x_] := E^-x
Plot[{f[x], g[x]}, {x, -3, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -3, -2}, WorkingPrecision -> 110]
r = x /. FindRoot[f[x] == g[x], {x, -2, -1}, WorkingPrecision -> 110]
r = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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