Limit Question: Solving with a Helpful Link

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SUMMARY

The discussion centers on solving a limit problem involving the function (1 + x)^(1/x). A user provided a link to an image illustrating their approach, which was deemed incorrect due to a miscalculation in the derivative. The correct method involves using logarithmic differentiation, specifically Log[(1 + x)^(1/x)] = Log[1+x] / x, leading to the conclusion that the derivative can be expressed as f'(x) = y f(x).

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That answer is not the limit, it's what you would have gotten had you taken the derivative correctly.

To find the derivative of (1 + x)^(1/x) write Log[(1 + x)^(1/x)] = Log[1+x] / x. Say this has derivative y, which means (Log f(x))' = y = f'(x)/f(x), so f'(x) = y f(x).
 

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