Let e denote the base of the natural logarithm. The value of the re...

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Let e denote the base of the natural logarithm. The value of the real number a for which the right hand limit
\( \mathrm{P} \)
\[
\lim _{x \rightarrow 0^{+}} \frac{(1-x)^{\frac{1}{x}}-e^{-1}}{x^{a}}
\]
W
is equal to a nonzero real number, is
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