query: Evaluating $\lim_{x\to ∞}\left (\sqrt{x^2+4x+1}-x\right)$
positive_passages.docid: 13148
positive_passages.text: Limits: How to evaluate $\lim\limits_{x\rightarrow \infty}\sqrt[n]{x^{n}+a_{n-1}x^{n-1}+\cdots+a_{0}}-x$
negative_passages.docid: 8387
negative_passages.text: Evaluate $\lim_{n \rightarrow \infty} \frac {[(n+1)(n+2)\cdots(n+n)]^{1/n}}{n}$
negative_passages.docid: 126749
negative_passages.text: Evaluate $\lim_{x \rightarrow 0} x^x$
negative_passages.docid: 105860
negative_passages.text: Evaluate the limit of $(n+1)\int_0^1x^n\ln(1+x)\,dx$ when $n\to\infty$
negative_passages.docid: 54893
negative_passages.text: $ \lim\limits_{x \rightarrow \ + \infty}(\sqrt{x^2 + 2x} - \sqrt{x^2 - 7x})$
negative_passages.docid: 18353
negative_passages.text: Evaluate of $\lim_{n\rightarrow \infty}\left(\frac{n+1}{n}\right)^{n^2}\cdot \frac{1}{e^n}$
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: 37251
negative_passages.text: Values of the limit $\lim\limits_{x\to+\infty}\left(\sqrt{(x+a)(x+b)}-x\right)$
negative_passages.docid: 104365
negative_passages.text: Evaluate: $\lim_{n\to\infty}\left({2\sqrt n}-\sum_{k=1}^n\frac1{\sqrt k}\right)$
negative_passages.docid: 37755
negative_passages.text: Limit $\lim_{x \to \infty}{\sin{\sqrt{x+1}}-\sin{\sqrt{x}}}$
negative_passages.docid: 144403
negative_passages.text: Limit $\lim_{x\rightarrow +\infty}\sqrt{x}e^{-x}\left(\sum_{k=1}^{\infty}\frac{x^{k}}{k!\sqrt{k}}\right)$
negative_passages.docid: 127001
negative_passages.text: Evaluate $\lim_{x\to \infty} \cos (\sqrt {x+1})-\cos (\sqrt x)$
negative_passages.docid: 156546
negative_passages.text: Evaluate the limit $\lim_{n\rightarrow \infty}\frac{1}{\sqrt{n}}\left(1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\ldots+\frac{1}{\sqrt{n}}\right)$
negative_passages.docid: 43703
negative_passages.text: Find $\lim _{x\to \infty }\left(x\left(\ln\left(x+1\right)-\ln x\right)\right) $
negative_passages.docid: 26211
negative_passages.text: Computing $\lim_{x \to \infty} x \biggl[ \frac{1}{e} - \left( \frac{x}{x+1} \right)^x \biggr]$
negative_passages.docid: 48985
negative_passages.text: Calculating $\lim_{x\to+\infty}(\sqrt{x^2-3x}-x)$
negative_passages.docid: 42241
negative_passages.text: Evaluation of $\lim_{n\rightarrow \infty}\sum^{n}_{r=1}\frac{r}{n^2+n+r}$