Evaluate: `("lim")_(nvec0)(e-(1+x)^(1/x))/x`

Evaluate lim_(xto0) (e-(1+x)^(1//x))/(x) .

Evaluate: lim_(x rarr0)(e-(1+x)^((1)/(x)))/(x)

Evaluate: lim_(x rarr0)((1+x)^((1)/(x))-e+(1)/(2)ex)/(x^(2))

Evaluate lim_(xto0) ((1+x)^(1//x)-e+(1)/(2)es)/(x^(2)) .

Slove lim_(xto0)((1+x)^(1//x)-e)/x

The value of lim_(xto 0)(e-(1+x)^(1//x))/(tanx) is

(lim)_(x->0)[((1+x)^(1//x))/e]^(1//x)\ \

lim_(xto0)((e^(x)-1)/x)^(1//x)

Evaluate: (lim)_(x rarr e)(log x-1)/(x-e)

Evaluate: (i)lim_(xrarr0)((e^(-x)-1)/(x))(ii)lim_(xrarr0)((e^(x)-e^(-x))/(x))(iii)lim_(xrarr0)((e^(x)+e^(-x)-2)/(x^(2)))