LIMITS (using \( L^{\prime} \) Hospital's rule \( \mathrm{P} \) \( ...

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LIMITS (using \( L^{\prime} \) Hospital's rule
\( \mathrm{P} \) \( \lim _{x \rightarrow a} \frac{x^{a}-a^{x}}{x^{x}-a^{a}} \) is equal to

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(1) \( \frac{1+\log _{e} a}{1-\log _{e} a} \)
(2) \( \frac{\log _{e}(e / a)}{\log _{e}(a e)} \)
(3) \( \frac{\log _{e}(e / e)}{\log _{e}(a e)} \)
(4) None of these
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