Let \( P_{n}=a^{P_{n-1}}-1, \forall n=2,3, \ldots \ldots \) and Let \( P_{1}=a^{x}-1 \) where \(...
Let \( P_{n}=a^{P_{n-1}}-1, \forall n=2,3, \ldots \ldots \) and Let \( P_{1}=a^{x}-1 \) where \( a \in R^{+} \). Evaluate \( \lim _{x \rightarrow 0} \frac{P_{n}}{x} \).
(a) \( \left[\ln \frac{1}{a}\right]^{n} \)
(b) \( (\ln a)^{n} \)
(c) \( [\ln (e a)-1]^{n} \)
(d) \( (\ln \mathrm{a})^{1 / n} \)
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