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Rewrite the limit using the identity: $a^x=e^{x\ln\left(a\right)}$
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$\lim_{x\to\infty }\left(e^{\frac{1}{3}x\ln\left(1+2x\right)}\right)$
Learn how to solve limits to infinity problems step by step online. Find the limit of (1+2x)^(1/3x) 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. The limit of the product of a function and a constant is equal to the limit of the function, times the constant: \displaystyle \lim_{t\to 0}{\left(at\right)}=a\cdot\lim_{t\to 0}{\left(t\right)}.