JEE Math Practice Question
Let $e$ denote the base of the natural logarithm. What is 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?
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