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A200626
Decimal expansion of the lesser of two values of x satisfying 5*x^2 - 4 = tan(x) and 0 < x < Pi/2.
3
1, 0, 8, 6, 2, 4, 8, 3, 0, 7, 3, 7, 2, 3, 5, 1, 4, 9, 3, 0, 5, 1, 6, 5, 3, 7, 4, 7, 0, 2, 5, 7, 9, 0, 1, 3, 0, 2, 1, 1, 1, 2, 7, 3, 5, 5, 4, 3, 6, 3, 1, 5, 1, 1, 7, 1, 8, 9, 4, 2, 5, 9, 8, 4, 9, 7, 6, 9, 4, 5, 4, 7, 8, 5, 2, 6, 3, 5, 8, 1, 9, 0, 8, 9, 9, 5, 8, 4, 4, 2, 6, 6, 5, 2, 0, 8, 5, 4, 8
OFFSET
1,3
COMMENTS
See A200614 for a guide to related sequences. The Mathematica program includes a graph.
EXAMPLE
lesser: 1.0862483073723514930516537470257901302111...
greater: 1.4001025553369417418319593715715854730538...
MATHEMATICA
a = 5; c = 4;
f[x_] := a*x^2 - c; g[x_] := Tan[x]
Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .9, 1.0}, WorkingPrecision -> 110]
RealDigits[r] (* A200626 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
RealDigits[r] (* A200627 *)
CROSSREFS
Cf. A200614.
Sequence in context: A365254 A021847 A029684 * A360166 A197732 A224237
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Nov 20 2011
STATUS
approved