Find the following limit using expansion `lim_(x->0) ((ln(1+x)^(1+x))/(x^2)-1/x)`

Find the following limits: lim_(xrarrinfty)(e^(1/x))^(ln(1+x))

Find the following limits: lim_(xrarr0)((x^2+2x-1)/(x^2-1))^(1/x)

Find limit of the following if it exists: lim_(xto0)(log_(e)(1+2x))/(x)

Evaluate the following limits . Lim_(x to 0) ((1+x)^(6)-1)/((1+x)^(2)-1)

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))

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))

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))

Evaluate the following limits : lim_(x to 0)(log(1+x))/(e^(x)-1) .

Find limit of the following if it exists: lim_(xto0)(log(1+x^(3)))/(sin^(3)x)

Evaluate the following limit : lim_(x rarr 0) (sqrt(1+x)-sqrt(1-x))/(x) .