Given that e=lim⁡x→∞(1+1x)xe=\displaystyle\lim_{x \rightarrow \infty} \left( 1+\frac{1}{x} \right)^x, evaluate lim⁡x→0(1+2x)1x.\lim_{x \rightarrow 0} (1+2x)^{\frac{1}{x}}.

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