1
vote
2answers
72 views

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 ...
0
votes
2answers
47 views

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=.....
2
votes
2answers
65 views

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 ...
3
votes
2answers
134 views

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 ...
4
votes
4answers
401 views

Of all the possible combinations of positive numbers that sum to 10, which has the largest multiplication?

Of all the possible combinations of positive numbers that sum to 10, which has the largest multiplication? I had also got a clue: it's related to e. Please help! ...