query: Compute $\lim_{x\to\infty}x\;\left[\left(1+\frac{1}{x}\right)^x-e\right]$
positive_passages.docid: 44668
positive_passages.text: Limit of $x\left(\left(1 + \frac{1}{x}\right)^x - e\right)$ when $x\to\infty$
negative_passages.docid: 49102
negative_passages.text: Evaluating $\lim_{n \to \infty}\left({^n\mathrm{C}_0}{^n\mathrm{C}_1}\dots{^n\mathrm{C}_n}\right)^{\frac{1}{n(n+1)}}$
negative_passages.docid: 48041
negative_passages.text: Compute the given limit as $x$ approaches $\infty$
negative_passages.docid: 64169
negative_passages.text: Why isn't $\lim \limits_{x\to\infty}\left(1+\frac{1}{x}\right)^{x}$ equal to $1$?
negative_passages.docid: 49012
negative_passages.text: How to evaluate $\lim_{x \to \infty}\left(\sqrt{x+\sqrt{x}}-\sqrt{x-\sqrt{x}}\right)$?
negative_passages.docid: 53719
negative_passages.text: Evaluate $\lim_{x \to 0} \left(\frac{1}{\ln(1+x)} + \frac{1}{\ln(1-x)}\right)$
negative_passages.docid: 156557
negative_passages.text: How to compute $\lim_{n\rightarrow\infty}e^{-n}\left(1+n+\frac{n^2}{2!}\cdots+\frac{n^n}{n!}\right)$
negative_passages.docid: 11622
negative_passages.text: Find $\lim _{n\to \infty }\left(\frac{1}{n^2+1}+\frac{1}{n^2+2}+...+\frac{1}{n^2+n}\right)$
negative_passages.docid: 122769
negative_passages.text: Show that $\lim_{n\to \infty}\int_{[0,\infty]}\left(1+\dfrac{x}{n}\right)^n\exp(-ax)=\dfrac{1}{a-1}$
negative_passages.docid: 74919
negative_passages.text: Finding limit of function $\lim_{x\to 0}\left(\frac{(1+x)^\frac1x}{e}\right)^\frac1x$
negative_passages.docid: 54830
negative_passages.text: Find the limit $\lim\limits_{x\to\infty} f(x)= \lim\limits_{x \to \infty} \left(\frac{x}{x+1}\right)^x$
negative_passages.docid: 139215
negative_passages.text: Find the value of $\lim_{x \to - \infty} \left( \sqrt{x^2 + 2x} - \sqrt{x^2 - 2x} \right)$
negative_passages.docid: 35260
negative_passages.text: Evaluate the limit $\displaystyle\lim_{x \to 0}\frac{(e-\left(1 + x\right)^{1/x})}{\tan x}$.
negative_passages.docid: 113537
negative_passages.text: Limit $\lim_{n\to\infty}\left(1-\frac{1}{3}\right)^2\left(1-\frac{1}{6}\right)^2\cdots\left(1-\frac{1}{\frac{n(n+1)}{2}}\right)^2$
negative_passages.docid: 76638
negative_passages.text: Find the limit $ \lim_{n \to \infty}\left(\frac{a^{1/n}+b^{1/n}+c^{1/n}}{3}\right)^n$
negative_passages.docid: 51884
negative_passages.text: Compute: $\lim\limits_{n\to+\infty}\int\limits_{0}^1 e^{\{nx\}}x^{100}dx$
negative_passages.docid: 49128
negative_passages.text: How to prove $\lim\limits_{n \to \infty} (1+\frac1n)^n = e$?