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Limits involving the definition of the natural constant e

Solution to Elementary Analysis: The Theory of Calculus Second Edition Section 30 Exercises 30.5 Solution: We start by showing that $$\label{30-5-1} \lim_{x\to 0}\left(1+x\right)^{1/x}=e.$$ Indeed, note that  \left(1+x\right)^{1/x}=e^{ \ln\left(1+x\right)^{1/x}…