query: Evaluate $\lim\limits_{x\to\infty}(\sin\sqrt{x+1}-\sin\sqrt{x})$
positive_passages.docid: 37755
positive_passages.text: Limit $\lim_{x \to \infty}{\sin{\sqrt{x+1}}-\sin{\sqrt{x}}}$
negative_passages.docid: 18079
negative_passages.text: Evaluating $\lim\limits_{x\to \infty}\sqrt[6]{x^{6}+x^{5}}-\sqrt[6]{x^{6}-x^{5}}$
negative_passages.docid: 118893
negative_passages.text: Calculate the limit: $\lim_{x\to\infty} \sqrt[x]{3^x+7^x}$
negative_passages.docid: 9541
negative_passages.text: Evaluate $\lim_{n\to\infty}\frac {qn+1}{qn} \frac {qn+p+1}{qn+p} \cdots \frac {qn+np+1}{qn+np}$ where $p\in\mathbb{N}\setminus\{0,1\},q>0.$
negative_passages.docid: 128063
negative_passages.text: How to evaluate the limit $\lim_{x\to 0} \frac{1-\cos(4x)}{\sin^2(7x)}$
negative_passages.docid: 51281
negative_passages.text: Evaluating Limit Question $\lim\limits_{n\to \infty}\ \frac{1+\sqrt[2]{2}+\sqrt[3]{3}+\cdots+\sqrt[n]{n}}{n}=1$?
negative_passages.docid: 101536
negative_passages.text: Difficult limit evaluation: $\lim_{x\to\infty}(\sqrt{x^2+4x} - x)$
negative_passages.docid: 17069
negative_passages.text: Limit $\lim_{x\to \infty} \frac{\sqrt{x+1}+\sqrt{x+2}-\sqrt{4x+12}}{\sqrt{x+2}+\sqrt{x}-\sqrt{4x+12}}$
negative_passages.docid: 138169
negative_passages.text: Finding $\lim\limits_{n \to \infty }n\int_{0}^{1}\frac{x^{n}}{1+x+x^{n}}dx$
negative_passages.docid: 154286
negative_passages.text: Evaluating $\lim_{n \to \infty} (1 + 1/n)^{n}$
negative_passages.docid: 41203
negative_passages.text: Finding $\lim\limits_{x \to \infty} (\sqrt{9x^2+x} - 3x)$
negative_passages.docid: 76342
negative_passages.text: Find the limit: $\displaystyle\lim_{x\to \infty} (\sqrt{x^2+x}-\sqrt{x^2-x})$.
negative_passages.docid: 98501
negative_passages.text: How to evaluate $ \lim_{x\rightarrow +\infty } \sqrt[x]{a^x+b^x} = ? $
negative_passages.docid: 45537
negative_passages.text: Finding the limit $\lim_{x\rightarrow \infty} \sqrt[3]{x+1}-\sqrt[3]{x}$
negative_passages.docid: 18156
negative_passages.text: Find $\lim_{x\to \infty} \ln(x+1)/(\ln(x))$
negative_passages.docid: 40227
negative_passages.text: Compute $\lim\limits_{n\to\infty}n^2\left(\left(1+\frac1{n+1}\right)^{n+1}-\left(1+\frac1n\right)^n\right)$
negative_passages.docid: 65975
negative_passages.text: Calculating $\lim_{n\to\infty}\sqrt{n}\sin(\sin...(\sin(x)..)$