lim_(x rarr0)(e^(2x)-1)/(3x)=

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Using lim_(x rarr 0) (e^(x)-1)/(x)=1, deduce that, lim_(x rarr 0) (a^(x)-1)/(x)=log_(e)a [agt0].

lim_(x rarr0)(2^(2x)-1)/(x)

Evaluate : lim_(x rarr0)(a^(2x)-1)/(x)

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

The value of lim_(x rarr0)(e^(x)-1)/(x) is-

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

Prove quad that quad (i) lim_(x rarr0)(a^(x)-1)/(x)=log_(e)aquad (ii) lim_(x rarr0)(log_(1+x))/(x)=1

Use formula lim_(x rarr0)(a^(x)-1)/(x)=log(a) to find lim_(x rarr0)(2^(x)-1)/((1+x)^((1)/(2))-1)

lim_(x rarr0)(2^(5x)-1)/(x)

The value of lim_(x rarr 0) ((e^(x)-1)/x)