Question

Let e denote the base of the natural logarithm. The value of the real number a for which the right hand limit
$\displaystyle\lim_{x\rightarrow 0^+} \frac{(1-x)^{\frac{1}{x}} - e^{-1}}{x^a}$
is equal to a nonzero real number, is_____

Answer 1

$\text{a non-zero real number, is}\; \underline{1}.$