`lim_(x rarr 0) (a^x - 1)/x`

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

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

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

Show that : 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

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

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

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

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

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