Using `underset(xrarr0)"lim"(e^(x)-1)/(x)=1" deduce that ," underset(xrarr0)"lim"(a^(x)-1)/(x)=log_(e)a[agt0].`

underset(xrarr0)"lim"(e^(3x)-1)/(x) =

underset(xrarr0)"lim"(a^(2x)-1)/(x) =

underset (xrarr0)lim x^(x)

underset(xrarr0)"lim"(log(1+4x))/(x) =

Prove that underset(xrarr0)lim (a^x-1)/x= log a .

Evaluate : underset(xrarr0)"lim"(tanx^(@))/(x)

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

Starting from underset(xrarra)"lim"(x^(n)-a^(n))/(x-a)=na^(n-1)" deduce that ," underset(xrarr0)"lim"((1+x)^(n)-1)/(x)=n.

Evaluate : underset(xrarr0)"lim"(1)/(x) .

underset(xrarr0)lim (e^x -1)/(x) is equal to