# Tagged Questions

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### Limit of ${x}^{\frac1{1-x}}$ as $x$ approaches 1

I have the following homework question, and I've been stuck on it for the last 2 hours. I have no idea how to find the answer. $$\lim\limits_{x\to1} {x}^{\frac1{1-x}}$$ I have tried manipulating the ...
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### How to isolate a variable when its on both sides of equation

$ex-1=x$ How do rearrange this equation to isolate x i.e in the form of x=.....
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### Evaluate $a^i$ where $a$ is real:

I have a question involving the evaluation of $3^i$, but I am unsure how to do this. I know how to solve such questions involving $e^{i\theta}$, but how does this work with a different base? (I ...
### Need to show that $\lim_{x\to\infty}\left(\sum_{n\le x}^{}\frac{1}{n}-\ln x \right)$ exist and is less than $1$ [duplicate]
Need some help here. I need prove that the following limit exist and is less than $1$ $$\lim_{x\to\infty}\left(\sum_{n\le x}^{}\frac{1}{n}-\ln x\right)$$ I feel a little lost here, this is my first ...