query: How to Solve $\lim_{x\to \infty}\sqrt{x^2 + ax} - \sqrt{x^2 + bx}$
positive_passages.docid: 18079
positive_passages.text: Evaluating $\lim\limits_{x\to \infty}\sqrt[6]{x^{6}+x^{5}}-\sqrt[6]{x^{6}-x^{5}}$
negative_passages.docid: 36648
negative_passages.text: The limit of $((1+x)^{1/x} - e+ ex/2)/x^2$ as $x\to 0$
negative_passages.docid: 76560
negative_passages.text: How do I calculate this limit: $\lim\limits_{n\to\infty}1+\sqrt[2]{2+\sqrt[3]{3+\dotsb+\sqrt[n]n}}$?
negative_passages.docid: 106087
negative_passages.text: Finding $\lim_{n \to \infty} \int_1^a \frac{n}{1+x^n} \, dx$
negative_passages.docid: 103833
negative_passages.text: limit $\lim_{n\to \infty }\sum_{k=1}^{n}\frac{k}{k^2+n^2}$
negative_passages.docid: 140622
negative_passages.text: Find the value of : $\lim_{x \to \infty} \sqrt{4x^2 + 4} - (2x + 2)$
negative_passages.docid: 113913
negative_passages.text: using L'Hospital solve $\lim_{x \to \infty} x - x^{2}\ln(1 + \frac{1}{x})$
negative_passages.docid: 109540
negative_passages.text: Simplify limit problem $\lim\limits_{x\to 0}\frac{\sqrt{2+x^2}-\sqrt{2+x^2}}{x^2}$
negative_passages.docid: 19631
negative_passages.text: Finding $\lim_{n\to \infty}\sqrt n \int_0^1 \frac{\,dx}{(1+x^2)^n}$
negative_passages.docid: 150734
negative_passages.text: Solving $\lim\limits_{x\to0} \frac{x - \sin(x)}{x^2}$ without L'Hospital's Rule.
negative_passages.docid: 37277
negative_passages.text: $\lim\limits_{n \to{+}\infty}{\sqrt[n]{n!}}$ is infinite
negative_passages.docid: 65975
negative_passages.text: Calculating $\lim_{n\to\infty}\sqrt{n}\sin(\sin...(\sin(x)..)$
negative_passages.docid: 46156
negative_passages.text: How to find $\lim_{x \to \infty} [x]/x$?
negative_passages.docid: 133244
negative_passages.text: Finding $\lim_{n \to \infty} n(\sqrt[n]{2} - 1)$
negative_passages.docid: 158447
negative_passages.text: Limit as $(x,y)$ approaches $(0,0)$ of $(1+x^2+y^2)^{\frac{1}{x^2+y^2+xy^2}}$
negative_passages.docid: 53014
negative_passages.text: Solve $(\alpha,\beta)$ for $\lim_{n\to\infty} \frac{\sqrt[n^2]{1!2!\cdots n!}}{n^\alpha} = \beta$
negative_passages.docid: 48041
negative_passages.text: Compute the given limit as $x$ approaches $\infty$