" 31."lim(x rarr0)(a^(x)-b^(x))/(x)=log(...

" 31."lim_(x rarr0)(a^(x)-b^(x))/(x)=log_(e)((a)/(b))quad " (UP) "

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lim_(x rarr 0) (a^(x)-b^(x))/x =

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

lim_(x rarr0)((a^(x)-1)/(x))=log_(e)a

lim_(x rarr 0) (a^x-b^x)/x=

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

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

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

lim_(x rarr0)(e^(x)-log(ex+e))/(x)

lim_(x rarr 0) (a^(x)-b^(x))/(e^(x)-1) =

lim_(x rarr0)(cotx)^(x)

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