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Lim x tends to 0 (x-sin x) / x ^ 3
Original formula = LIM (1 - cos x) / 3x ^ 2 (x - > 0)
= lim sinx / 6x ( x -> 0)
= lim cosx / 6 ( x -> 0)
= 1 / 6
It is proved that when 0 is less than X and less than 2 / 2 π, TaNx is greater than x + (1 / 3) x cube
First aid
Expand Tan (x) at 0 with Taylor formula
tan(x) = x + x^3/3 + 2*x^5/3 +……
Because x > 0,
So tan (x) is greater than x + x ^ 3 / 3
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