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** Step-by-step Solution **

Problem to solve:

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Rewrite the limit using the identity: $a^x=e^{x\ln\left(a\right)}$

Learn how to solve limits to infinity problems step by step online.

$\lim_{x\to\infty }\left(e^{\frac{1}{x}\ln\left(x\right)}\right)$

Learn how to solve limits to infinity problems step by step online. Find the limit of x^(1/x) as x approaches infinity. Rewrite the limit using the identity: a^x=e^{x\ln\left(a\right)}. Multiplying the fraction by \ln\left(x\right). Apply the power rule of limits: \displaystyle{\lim_{x\to a}f(x)^{g(x)} = \lim_{x\to a}f(x)^{\displaystyle\lim_{x\to a}g(x)}}. The limit of a constant is just the constant.

** Final Answer

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