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Show that 2 sin x + than x ge 3x all x in (0, pi/20). |
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Answer» SOLUTION :Let `F(x) = 2 sin x + tan x - 3x` Then `f.(x) = 2 cos x + sec^2 x - 3` Now `f.(x) GT 0 for all x in (0,pi/2)`. Thus `f.(x) is INCREASING in (0,pi/2). But `F(0) = 0` Thus `f(x) ge 0 for all x in (0, pi/2)` `rArr 2 sin x + tan x - 3x ge 0 for all x in (0, pi/2)cdot . `2 sin x + tan x ge 3x for all x in (0,pi/2). |
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