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A196915
Decimal expansion of the slope (negative) at the point of tangency of the curves y=1/(1+x^2) and y=c*cos(x), where c is given by A196914.
3
6, 0, 7, 6, 2, 2, 2, 3, 7, 6, 9, 6, 8, 6, 8, 6, 5, 8, 5, 9, 0, 0, 1, 0, 0, 2, 6, 8, 2, 0, 2, 6, 3, 6, 4, 3, 2, 2, 7, 4, 8, 0, 9, 8, 7, 7, 7, 6, 5, 9, 7, 7, 8, 9, 9, 8, 2, 6, 0, 9, 5, 9, 6, 0, 2, 6, 2, 7, 3, 3, 6, 3, 0, 4, 6, 2, 8, 4, 7, 5, 8, 1, 4, 8, 2, 6, 6, 5, 4, 7, 4, 8, 5, 6, 0, 2, 5, 6, 6
OFFSET
0,1
EXAMPLE
x=-0.60762223769686865859001002682026364322748...
MATHEMATICA
Plot[{1/(1 + x^2), 0.874*Cos[x]}, {x, .5, 1}]
t = x /. FindRoot[Tan[x] == 2 x/(1 + x^2), {x, .5, 1}, WorkingPrecision -> 100]
RealDigits[t] (* A196913 *)
c = N[Sqrt[t^4 + 6 t^2 + 1]/(t^4 + 2 t^2 + 1), 100]
RealDigits[c] (* A196914 *)
slope = N[-c*Sin[t], 100]
RealDigits[slope] (* A196915 *)
CROSSREFS
Sequence in context: A341906 A365163 A195432 * A374407 A249651 A021626
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Oct 07 2011
STATUS
approved