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Numerade Educator



Problem 56 Hard Difficulty

Show that $ \displaystyle \lim_{n \to x} (1 + \frac {x}{n})^n = e^x $ for any $ x > 0. $


Therefore $\lim _{\lim _{\infty}}\left(1+\frac{x}{n}\right)^{n}=\lim _{m \rightarrow \infty}\left(1+\frac{1}{m}\right)^{m x}=\left[\lim _{m \rightarrow \infty}\left(1+\frac{1}{m}\right)^{m}\right]^{x}=e^{x}$
by Equation $6 .$

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Video Transcript

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