lim(x rarr0)(1)/(x)((1)/(sin x)-(1)/(tan...

lim_(x rarr0)(1)/(x)((1)/(sin x)-(1)/(tan x))=

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lim_(x rarr0)((1)/(x))^(sin x)

lim_(x rarr0)(a^(x)-1)/(sin x)=

lim_ (x rarr0) ((1) / (sin x) - (1) / (tan x))

lim_(x rarr0)((1)/(x))^(tan x)=

lim_(x rarr0)(1-x)^(1/x)=

lim_(x rarr0)(a^(sin x)-1)/(sin x)

lim_(x rarr0)((sin x)/(x))^((1)/(x))

lim_(x rarr0)x sin((1)/(x))

lim_(x rarr0)(1-cos x)/(sin x)

lim_(x rarr0)(sin x)/(x)=1

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