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A196833
Decimal expansion of the slope (negative) at the point of tangency of the curves y=1/(1+x^2) and y=c*sin(x), where c is given by A196832.
3
1, 2, 7, 0, 7, 1, 8, 4, 1, 1, 8, 6, 4, 4, 1, 9, 0, 5, 9, 4, 7, 9, 4, 4, 6, 4, 3, 3, 9, 3, 0, 0, 1, 7, 6, 8, 3, 8, 5, 6, 2, 5, 4, 4, 7, 1, 6, 6, 1, 6, 1, 6, 3, 2, 0, 7, 5, 0, 6, 4, 5, 8, 1, 2, 0, 3, 8, 7, 5, 4, 2, 8, 7, 7, 9, 2, 4, 1, 7, 9, 1, 2, 7, 7, 0, 9, 9, 2, 3, 3, 8, 2, 7, 6, 7, 3, 3, 4, 3, 7
OFFSET
0,2
EXAMPLE
x=-0.12707184118644190594794464339300176838562544...
MATHEMATICA
Plot[{1/(1 + x^2), .205 Sin[x]}, {x, 0, Pi}]
t = x /. FindRoot[x^2 + 2 x*Tan[x] + 1 == 0, {x, 2, 3}, WorkingPrecision -> 100]
RealDigits[t] (* A196831 *)
c = N[Csc[t]/(1 + t^2), 100]
RealDigits[c] (* A196832 *)
slope = N[c*Cos[t], 100]
RealDigits[slope] (* A196833 *)
CROSSREFS
Sequence in context: A325905 A372386 A199273 * A245224 A016638 A199398
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Oct 07 2011
STATUS
approved