The exponential function \(\RR\to\RR\), \(x\mapsto e^x\), is given by \[ e^x \coloneqq \lim_{n \to \infty} \qty{1 + \frac{x}{n}}^n, \] the limit existing for every \(x\in\RR\).
What is the limit definition of $e^x$?
Limit definition of exponential function
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