query: Expansion of $x\mapsto\left(\frac \pi 2 + \arcsin x\right)^2$ in powers of $x+1$
positive_passages.docid: 156312
positive_passages.text: Taylor expansion for $\arcsin^2{x}$
negative_passages.docid: 8913
negative_passages.text: Show that there is $\xi$ s.t. $f(\xi)=f\left(\xi+\frac{1}{n}\right)$
negative_passages.docid: 132610
negative_passages.text: Expand $\sqrt{1-x}$ up to and including the term $x^2$ (How should i proceed further)
negative_passages.docid: 53537
negative_passages.text: Evaluate $\lim_{n\rightarrow\infty}\sum_{k=1}^n\arcsin(\frac k{n^2})$
negative_passages.docid: 146349
negative_passages.text: $\int_0^\infty \frac{\ln\left(1+x-\sqrt{2x}\right)}{1+x^2}\,dx$
negative_passages.docid: 98367
negative_passages.text: Limit of $\left(\frac{n^2+2}{2n^2+1}\right)^{n^2}$
negative_passages.docid: 74692
negative_passages.text: Simple Power Series Expansion for Problems similar to $f = (1 + \epsilon \,x)^{1/\epsilon}$
negative_passages.docid: 60559
negative_passages.text: How prove this $x^3<\sin^2{x}\tan{x},x\in\left(0,\dfrac{\pi}{2}\right)$
negative_passages.docid: 57670
negative_passages.text: Show that $|z_1 + z_2|^2 < (1+C)|z_1|^2 + \left(1 + \frac{1}{C}\right) |z_2|^2$
negative_passages.docid: 44095
negative_passages.text: Prove that $\lim_{x\to \infty}\left(x-\ln\cosh x\right)=\ln 2$
negative_passages.docid: 77821
negative_passages.text: Taylor series expansion of function $f(x) = \frac{\arcsin(x)}{\sqrt{1-x^2}}$
negative_passages.docid: 80553
negative_passages.text: Show that,$\int_0^\pi \left|\frac{\sin nx}{x}\right|\mathrm{d}x \ge \frac{2}{\pi}\left(1+\frac12+\cdots+\frac{1}{n}\right)$
negative_passages.docid: 7500
negative_passages.text: $\arctan$ of a square root as a rational multiple of $\pi$
negative_passages.docid: 1859
negative_passages.text: Proving $\arctan(\sqrt{x^2+1}-x)=\frac{\pi}{4}-\frac{1}{2}\arctan(x)$
negative_passages.docid: 69673
negative_passages.text: Prove that $\left (\frac{a^2 + b^2 +c^2}{a+b+c} \right) ^ {(a+b+c)} > a^a b^b c^c$
negative_passages.docid: 24311
negative_passages.text: Proving $\frac{\sin x}{x} =\left(1-\frac{x^2}{\pi^2}\right)\left(1-\frac{x^2}{2^2\pi^2}\right) \left(1-\frac{x^2}{3^2\pi^2}\right)\cdots$
negative_passages.docid: 36023
negative_passages.text: Showing that $ \sum_{n=1}^{\infty} \arctan \left( \frac{2}{n^2} \right) =\frac{3\pi}{4}$