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I am using maple to verify an expression, $x < \tan(x)$ for $0 < x < \pi/2$, but it returns FAIL, i.e.

is ( x < tan(x) ) assuming 0 < x < Pi/2

which returns FAIL.

I am very curious to know why this in-equality cannot be evealuated by Maple? I can evaluate is by computing the following

f := x -> tan(x) - x
g := x -> diff(f(x), x)
is (g(x) > 0) assuming 0 < x < Pi/2

which returns true.

Note1: Maple uses 3-valued logic for boolean operations, true, false and FAIL, where FAIL is returned whenever Maple is unable to evaluate a proposition with certainty.

Note2: Maple is a proprietary computer algebraic system that I have access through my university's lab.

Ali Shakiba
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  • Ali jan aya ino tu Mapleprime.com matrah kardi? Age jawabi naymad unja ham ye try bokon. :-) – Mikasa Feb 26 '14 at 16:31
  • Salam, hamin kar ro kardam. albate javab haye jalebi gereftam, vali yeki do rooz vaght verify kardaneshon ro nadaram. be mahze inke javab khoobi begiram, ersal mikonam inja. – Ali Shakiba Feb 27 '14 at 20:47
  • Mamnun. man montazeram. sign bede waghti jawab gerefti. :-) – Mikasa Feb 28 '14 at 06:49

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