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

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

lim_(x rarr0)[(log(1+x))/(x)]^((1)/(x)) equals-

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)(ln(1+x)^(1+x))/(x^(2))-(1)/(x)

lim_(x rarr0)[(ln(1+x)^(1+x))/(x^(2))-(1)/(x)]

a=lim_(x rarr0)(ln(cos2x))/(3x^(2)),b=lim_(x rarr0)(sin^(2)2x)/(x(1-e^(x))),c=lim_(x rarr1)(sqrt(x)-x)/(ln x)

lim_(x rarr 0) (log(1+x))/(3^x-1)=1/(log_(e)(3))

lim_(x rarr0)(log(1+x))/(3^(x)-1)

lim_(x rarr0)(log(1+x))/(3^(x)-1)