Category: Relation and Functions

Question Number 65383 by mathmax by abdo last updated on 29/Jul/19 $$1)calculate{\int }_0^{\mathrm{\infty }}\frac{dx}{1+e^{nx}}withnintegrnaturalandn⩾1$$$$2)concludethevalueof\sum _{k=1}^{\mathrm{\infty }}\frac{{(-1)}^{k-1}}{k}$$ Commented by mathmax…

Question Number 65297 by mathmax by abdo last updated on 28/Jul/19 $$let{U}_{n}asequencewichverify{U}_n+U_{n+1}+U_{n+2}=n{(-1)}^n$$$$forallintegrncalculateintermsofn$$$${A}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:\left(−\mathrm{1}\right)^{{k}} \:{U}_{{k}} \…

Question Number 130771 by mathmax by abdo last updated on 28/Jan/21 $$\mathrm{let}\mathrm{A}=\left(\begin{array}{c}12\\ 21\end{array}\right)$$$$1)\mathrm{find}{\mathrm{e}}^{\mathrm{A}}\mathrm{and}{\mathrm{e}}^{-\mathrm{A}}$$$$2)\mathrm{calculate}\mathrm{ch}\left(\mathrm{A}\right)\mathrm{and}\mathrm{sh}\left(\mathrm{A}\right)$$ Answered by Olaf last updated on…

Question Number 130726 by mathmax by abdo last updated on 28/Jan/21 $$\mathrm{find}{\lim }_{\mathrm{n}\to +\mathrm{\infty }}{\int }_0^{\mathrm{n}}{(1-\frac{\mathrm{t}}{\mathrm{n}})}^{\mathrm{n}}\arctan \left(\frac{2}{\mathrm{x}}\right)\mathrm{dx}$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 130699 by LYKA last updated on 28/Jan/21 Answered by MJS_new last updated on 28/Jan/21 $$z=\ln (x-2y+3)$$$$x-2y+3>0\iff y<\frac{x}{2}+\frac{3}{2}\wedge x\in \mathbb{R}\Rightarrow z\in \mathbb{R}$$ Terms of Service Privacy…