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show that if $x $ is an element of $\mathbb R$ then $$\lim_{n\to\infty} \left(1 + \frac xn\right)^n = e^x $$

(HINT: Take logs and use L'Hospital's Rule)

i'm not too sure how to go about answer this or putting it in the form $\frac{f'(x)}{g'(x)}$ in order to apply L'Hospitals Rule.

so far i've simply taken logs and brought the power in front leaving me with $$ n\log \left(1+ \frac xn\right) = x $$

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    I think, I saw something like this before at the site.2012-12-28
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    @BabakSorouh. Yes definitley2012-12-28
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    @BabakSorouh do either of you remember the question title by any chance?2012-12-28
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    Possible duplicate: http://math.stackexchange.com/questions/39170/how-come-such-different-methods-result-in-the-same-number-e2012-12-28
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    Sometimes this is the _definition_ of $e^x$. What is your definition of $e^x$?2012-12-28
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    @JulianKuelshammer: The problems are similar, but depending on the actual definition used for $e$, the answers could be different.2012-12-28

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