query: Evaluating $\sqrt2^{\sqrt2^{\sqrt2^{\:^{.^{\:^{.^{\: \infty}}}}}}}$
positive_passages.docid: 20532
positive_passages.text: Are these solutions of $2 = x^{x^{x^{\:\cdot^{\:\cdot^{\:\cdot}}}}}$ correct?
negative_passages.docid: 124699
negative_passages.text: How to calculate $\lim_{n \to \infty}\sqrt[n]{\frac{2^n+3^n}{3^n+4^n}}$
negative_passages.docid: 77721
negative_passages.text: Is it possible to compute $\int_1^{+ \infty} \frac{dx}{x^2(1+e^x)}$?
negative_passages.docid: 98501
negative_passages.text: How to evaluate $ \lim_{x\rightarrow +\infty } \sqrt[x]{a^x+b^x} = ? $
negative_passages.docid: 104878
negative_passages.text: What is the limit $\lim\limits_{n \to \infty} \frac{n^{\sqrt{n}}}{2^n}$?
negative_passages.docid: 123295
negative_passages.text: How does one evaluate $\sqrt[3]{x + iy} + \sqrt[3]{x - iy}$?
negative_passages.docid: 25646
negative_passages.text: What is the result of $\infty - \infty$?
negative_passages.docid: 149601
negative_passages.text: $\lim_{x\to{\infty}} (x-\sqrt{x^2+x})$
negative_passages.docid: 35861
negative_passages.text: Evaluate $\int_0^\infty\frac{\ln x}{1+x^2}dx$
negative_passages.docid: 63956
negative_passages.text: Evaluate $\int_0^{\infty}\frac{\ln x}{x^a(x+1)}dx$ where $0<a<1$
negative_passages.docid: 63023
negative_passages.text: Evaluation of $\lim_{x\rightarrow \infty}\sqrt{x^2+x+1} -\lfloor \sqrt{x^2+x+1 }\rfloor\;,$
negative_passages.docid: 124440
negative_passages.text: Evaluate this power series
negative_passages.docid: 84147
negative_passages.text: Evaluating $\sum_{n=1}^\infty \frac{2^{2n-1}}{5^{n+1}}$
negative_passages.docid: 114220
negative_passages.text: Find the value of $\large i^{i^{.^{.^.}}}$
negative_passages.docid: 144039
negative_passages.text: Computing $ \int_0^{\infty} \frac{ \sqrt [3] {x+1}-\sqrt [3] {x}}{\sqrt{x}} \mathrm dx$
negative_passages.docid: 59667
negative_passages.text: Evaluating $\int_0^\infty\frac{\sin(x)}{x^2+1}\, dx$
negative_passages.docid: 114195
negative_passages.text: Evaluating $\int_0^\infty \frac{\log (1+x)}{1+x^2}dx$