Prove that (i)`lim_(x->0) (a^x-1)/x=log_e a` (ii) `lim_(x->0) log_(1+x)/x=1`

lim_(x rarr0)(log(1+x))/(x)=1

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

Find the value of |(lim_( x to 1) (x^x-1)/(x log x )) /( lim_( xto0) (log (1-3x))/x)|

lim_(x rarr0)(log_(e)(1+x))/(x)

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

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

5.Find the value of lim_(x->0) log(1+x)/(x)

5.Find the value of lim_(x->0) log(1+x)/(x)

Find the following limits: (i) lim_(xto0) (1-x)^((1)/(x))" "(ii) lim_(xto1) (1+log_(e)x)^((1)/(log_(e)x)) (iii)lim_(xto0) (1+sinx)^((1)/(x))

Use the formula lim_(x to 0 ) (a^(x) - 1) / x log_(e) a , to find lim_( x to 0) (2^(x)-1)/((1+x)^(1//2) - 1) .