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I have this problem: $\lim_{x\to \pm \infty} (1+\frac 1x)^x$

I understand everything except how to handle the $\pm \infty$. When I tried to solve it I reasoned like this, since both $1^\infty$ and $1^{-\infty}$ should be equal to one then the answer to the original question should be $1$. But the correct answer is $e$. I can solve problems like these when it's just $+\infty$ but how do I solve it when there is plus minus infinity? Any help is appreaciated.

Sembfi
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    " I can solve problems like these when it's just $+\infty$" : are you sure ? – TheSilverDoe Oct 09 '22 at 11:41
  • @TheSilverDoe Yes Edit: Well maybe not, is there a difference between positive infinity and just infinity? – Sembfi Oct 09 '22 at 11:42
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    Please provide feedback if youre going to downvote the post. What can I improve etc. – Sembfi Oct 09 '22 at 11:43
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    @Sembfi No, this is not the point, the fact is that $$\lim_{x \rightarrow +\infty} \left( 1 + \dfrac{1}{x}\right)^x=e$$ and if you think that the limit is $1$, you have to rethink about it. – TheSilverDoe Oct 09 '22 at 11:49
  • @TheSilverDoe Yes, you are right. After reading more about this, I realized that I was completely wrong. – Sembfi Oct 09 '22 at 12:55

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