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** Step-by-step Solution **

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

Learn how to solve factor problems step by step online.

$\lim_{x\to\infty }\left(e^{2x\ln\left(1+\frac{3}{x}\right)}\right)$

Learn how to solve factor problems step by step online. Find the limit of (1+3/x)^(2x) as x approaches infinity. Rewrite the limit using the identity: a^x=e^{x\ln\left(a\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. Rewrite the product inside the limit as a fraction.

** Final Answer

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