A196824 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 A196774.

6, 3, 4, 1, 6, 4, 9, 7, 0, 6, 9, 5, 8, 7, 7, 9, 5, 6, 1, 0, 2, 7, 4, 9, 8, 1, 1, 8, 6, 4, 0, 2, 3, 8, 0, 5, 5, 8, 2, 2, 4, 8, 4, 2, 8, 3, 9, 3, 2, 7, 5, 4, 5, 8, 4, 2, 1, 3, 3, 1, 7, 4, 7, 4, 1, 0, 3, 6, 3, 6, 2, 9, 9, 4, 1, 7, 8, 8, 6, 3, 1, 0, 0, 1, 9, 3, 6, 4, 8, 0, 6, 5, 8, 7, 6, 8, 4, 6, 6, 7, 1, 4, 5, 6, 8, 1

Offset: 0

Author

Clark Kimberling, Oct 06 2011

Keywords

• nonn
• cons

Examples

			slope=-0.6341649706958779561027498118640238055822484...
		

Crossrefs

Cf. A196823.

Programs

Mathematica

Plot[{1/(1 + x^2), -.094 + Cos[x]}, {x, 0, 1}]
t = x /. FindRoot[2 x == ((1 + x^2)^2) Sin[x], {x, .5, 1}, WorkingPrecision -> 100]
RealDigits[t]     (* A196822 *)
c = N[-Cos[t] + 1/(1 + t^2), 100]
RealDigits[c]     (* A196823 *)
slope = N[-Sin[t], 100]
RealDigits[slope] (* A196824 *)