Evaluating $\lim_{x\to \infty}(\frac{x}{x-1})^x$
57203
Prove that $\lim_{x \to \infty}\big(\frac{x}{x-1}\big)^x$ is also $e$.
95508
Evaluate $\lim\limits_{x\to 1}\frac{\sqrt x-x^2 }{1-\sqrt x}$
30181
Proving that $\lim\limits_{x \to 0}\frac{e^x-1}{x} = 1$
93408
Trying to show that $\ln(x) = \lim_{n\to\infty} n(x^{1/n} -1)$
105860
Evaluate the limit of $(n+1)\int_0^1x^n\ln(1+x)\,dx$ when $n\to\infty$
17872
Evaluate $\lim\limits_{n\to\infty}\frac{\sum_{k=1}^n k^m}{n^{m+1}}$
64169
Why isn't $\lim \limits_{x\to\infty}\left(1+\frac{1}{x}\right)^{x}$ equal to $1$?
74204
Evaluate $\lim_{n\to\infty}(1+x)(1+x^2)\cdots(1+x^{2n}),|x|<1$
66526
Find the limit of: $\lim_{n\to\infty} \frac{1}{\sqrt[n+1]{(n+1)!} - \sqrt[n]{(n)!}}$
136297
Evaluate $\lim_{x \to 1} \frac{\sqrt[3]{x} -1}{\sqrt{x} -1}$
141892
How to evaluate $\int_0^\infty \frac{1}{x^n+1} dx$
6304
Evaluate $\lim_{(x,y) \to (0,0), x+y \neq 0}{\frac{\ln(1-x-y)}{x+y} } $
4224
Evaluate limit of an integral: $\lim_{x\to \infty }\frac{1}{x}\int _0^x\:\frac{dt}{2+\cos t}$
101536
Difficult limit evaluation: $\lim_{x\to\infty}(\sqrt{x^2+4x} - x)$
117497
Compute the limit $\lim_{n \to \infty} \frac{n!}{n^n}$
108917
Use $\delta-\epsilon$ to show that $\lim_{n\to\infty} a^{\frac{1}{n}} = 1$?
156231
Computing $\lim\limits_{n\to\infty} \int_{0}^{\infty}\frac{\sin(x/n)}{(1+x/n)^{n}}\, dx$