query: Evaluate $\lim_{x\to0}\frac{e-(1+x)^\frac1x}{x}$
positive_passages.docid: 19263
positive_passages.text: Limit as $x\to 0$ of $\frac{(1+x)^{1/x}-e}{x}$
negative_passages.docid: 144273
negative_passages.text: Find $\lim_{n\to\infty} \frac{1}{n} \int_0^\infty f(x) e^{-a_n x} dx$
negative_passages.docid: 36384
negative_passages.text: Q: $\lim_{n\to \infty}\left(1 + \frac{1}{n}\right)^{n} = e$
negative_passages.docid: 74204
negative_passages.text: Evaluate $\lim_{n\to\infty}(1+x)(1+x^2)\cdots(1+x^{2n}),|x|<1$
negative_passages.docid: 5157
negative_passages.text: How to evaluate $ \lim_{(x,y)\to(0,0)}\frac{y^2\sin^2x}{x^4+y^4} $
negative_passages.docid: 60831
negative_passages.text: Need hint for $\lim_{x\to 0} \frac{(x+1)^\frac{1}{x}-e}{x}$
negative_passages.docid: 154286
negative_passages.text: Evaluating $\lim_{n \to \infty} (1 + 1/n)^{n}$
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: 53719
negative_passages.text: Evaluate $\lim_{x \to 0} \left(\frac{1}{\ln(1+x)} + \frac{1}{\ln(1-x)}\right)$
negative_passages.docid: 136297
negative_passages.text: Evaluate $\lim_{x \to 1} \frac{\sqrt[3]{x} -1}{\sqrt{x} -1}$
negative_passages.docid: 127001
negative_passages.text: Evaluate $\lim_{x\to \infty} \cos (\sqrt {x+1})-\cos (\sqrt x)$
negative_passages.docid: 98365
negative_passages.text: How to evaluate $\lim_{x \rightarrow \infty} \left(\left(\frac{x+1}{x-1}\right)^x -e^2\right){x}^2$
negative_passages.docid: 46990
negative_passages.text: $\lim_{x\to0}\frac{e^x-1-x}{x^2}$ using only rules of algebra of limits.
negative_passages.docid: 27195
negative_passages.text: Evaluating $\int_{0}^{1}\frac{1-x}{1+x}\frac{\mathrm dx}{\ln x}$
negative_passages.docid: 35861
negative_passages.text: Evaluate $\int_0^\infty\frac{\ln x}{1+x^2}dx$
negative_passages.docid: 79646
negative_passages.text: Compute $\lim_{n\to\infty}\frac{\tfrac{n}{1}+\tfrac{n-1}{2}+\dots+\tfrac{2}{n-1}+\tfrac{1}{n}}{\ln(n!)}$
negative_passages.docid: 27511
negative_passages.text: Prove that $\lim_{x \to \infty} \frac{\log(1+e^x)}{x} = 1$