Let \( c \) be the Champernowne's constant, or\( c = 0.123456789101112131415161718192021... \)
Show, without calculator aid, that \[ \sin(c) + \cos(c) + \tan(c) > 10c \]
Guilherme Dela Corte
2 years, 10 months ago
Oh wow, that is a surprising bound.
(Using Wolfram) Equality holds at \( x \approx 0.12408 \).
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Better approximation: \(x\approx0.12407932542544436\)
I don't see how exactly it is surprising. The 10 can be replaced with any arbitrary constant, and it would be a "cool bound".