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# Limites - 1 l m x sin x x =0 1 1 Como 1 < sin x < 1 para...

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1. ım x →∞ sin x x = 0 Como - 1 < sin x < 1 para todo x, luego - 1 x < sin x x < 1 x para x 6 = 0 . Puesto que l´ ım x →∞ - 1 x = l´ ım x →∞ - 1 x = 0, y del teo del sanduche podemos concluir que ım x →∞ sin x x = 0 2. ım x 0 1 - cos x x = ım x 0 (1 - cos x )(1 + cos x ) x (1 + cos x ) = ım x 0 sin 2 x x (1 + cos x ) = ım x 0 sin x x ım x 0 sin x 1 - cos x = 1 · 0 = 0 3. ım x 0 tan x x = ım x 0 sin x x (cos x ) = ım x 0 sin x x ım x 0 1 cos x = 1 · 1 = 1 4. ım x 0 ln(1 + x ) x = ım x 0 ln(1 + x ) 1 x = ln l´ ım x 0 (1 + x ) 1 x = ln e = 1 5. Sea: α = e x - 1 α + 1 = e x ln( α + 1) = x Si x 0 , α 0 Asi: ım

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Limites - 1 l m x sin x x =0 1 1 Como 1 < sin x < 1 para...

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