OFFSET
0,1
COMMENTS
Let B be the greatest x satisfying x=1/x+cot(1/x), so that B=0.364... Then
...
cot(1/x) < x < 1/x+cot(1/x) for all x > B; equivalently,
...
cot(x) < 1/x < x+cot(x) for 0 < x < 1/B = 2.7437....
...
These inequalities and those at A196503 supplement the trigonometric inequalities given in Bullen's dictionary cited below.
REFERENCES
P. S. Bullen, A Dictionary of Inequalities, Longman, 1998, pages 250-251.
EXAMPLE
B=0.364470368591040538004400214637816084912410...
1/B=2.7437072699922693825611220811203071372042...
MATHEMATICA
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Oct 03 2011
STATUS
approved