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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
$$\lim_{x \rightarrow 0^{+}}\frac{(1-x)^{\frac{1}{x}}- e^{-1}}{x^{a}}$$
is equal to a nonzero real number, is _____
Correct Answer: e
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