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

Explanation

`underset(xto0)lim(e-(1+x)^(1//x))/(x)=underset(xto0)lim(e-e^((1)/(x)log_(e)(1+x)))/(x)`
`=underset(xto0)lim(e-e^((1)/(x)(x-(x^(3))/(2)+(x^(3))/(3)+(x^(4))/(4)+...)))/(x)`
`=underset(xto0)lim(e-e.e^(-((x)/(2)+(x^(2))/(3)+(x^(3))/(4)+...)))/(x)`
`=-e.underset(xto0)lim(e^(-((x)/(2)-(x^(2))/(3)+(x^(3))/(4)......))-1)/(-((x)/(2)-(x^(2))/(3)+(x^(3))/(4)...)).(-((x)/(2)-(x^(2))/(3)+(x^(3))/(4)...))/(x)`
`=(e)/(2)`