query: How to solve this limit: $\lim_{x\to\infty}\sqrt{x+\sqrt{x}}-\sqrt{x-1}$
positive_passages.docid: 142575
positive_passages.text: Find the value of : $\lim_{x\to\infty} \sqrt{x+\sqrt{x}}-\sqrt{x}$
negative_passages.docid: 98501
negative_passages.text: How to evaluate $ \lim_{x\rightarrow +\infty } \sqrt[x]{a^x+b^x} = ? $
negative_passages.docid: 46542
negative_passages.text: How do I calculate $\lim_{x\to+\infty}\sqrt{x+a}-\sqrt{x}$?
negative_passages.docid: 30834
negative_passages.text: limit of $\lim\limits_{x \to \infty}((x+1)^a - x^a)$
negative_passages.docid: 149601
negative_passages.text: $\lim_{x\to{\infty}} (x-\sqrt{x^2+x})$
negative_passages.docid: 7
negative_passages.text: Find value of the limit: $\lim_{n\to \infty}\sqrt[n]{1^2+2^2+\cdots+n^2}$
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: 75571
negative_passages.text: Limit of $\sqrt x$ as $x$ approaches $0$
negative_passages.docid: 151593
negative_passages.text: Prove that the limit of $\sqrt{n+1}-\sqrt{n}$ is zero
negative_passages.docid: 109489
negative_passages.text: How to solve $ \lim_{n\to\infty} \frac {(n!)^\frac{1}{n}}{n} $?
negative_passages.docid: 127001
negative_passages.text: Evaluate $\lim_{x\to \infty} \cos (\sqrt {x+1})-\cos (\sqrt x)$
negative_passages.docid: 101716
negative_passages.text: Find this limit: $ \lim_{n \to \infty}{(e^{\frac{1}{n}} - \frac{2}{n})^n}$
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: 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: 148320
negative_passages.text: Find the limit $\lim_\limits{n\to{\infty}}n^2(\sqrt[n]{x}-\sqrt[{n + 1}]{x})$ and my inquiry about Stolz-Cesàro theorem
negative_passages.docid: 44507
negative_passages.text: How can I find $\lim_{n\to \infty} a_n$
negative_passages.docid: 17090
negative_passages.text: Compute $\lim_\limits{n\to\infty}a_n$ where $a_{n+2}=\sqrt{a_n.a_{n+1}}$