`lim_(x to 0)(ln(1+x))/(x^(2))+(x-1)/(x)=`

lim_(x to 0) {(log_(e)(1+x))/(x^(2))+(x-1)/(x)}=

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

lim_(x to 0)(xe^(x)-log(1+x))/(x^(2))=

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

Find the following limit using expansion lim_(x rarr0)((ln(1+x)^(1+x))/(x^(2))-(1)/(x))

Statement-1 : lim_(x to 0) (1 - cos x)/(x(2^(x) - 1)) = (1)/(2) log_(2) e . Statement : lim_(x to 0) ("sin" x)/(x) = 1 , lim_(x to 0) (a^(x) - 1)/(x) = log a, a gt 0

Statement-1 : lim_(x to 0) (1 - cos x)/(x(2^(x) - 1)) = (1)/(2) log_(2) e . Statement : lim_(x to 0) ("sin" x)/(x) = 1 , lim_(x to 0) (a^(x) - 1)/(x) = log a, a gt 0

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

Evaluate lim_(x to 0) (sinx+log(1-x))/(x^(2)).