Question Number 3055 by Filup last updated on 04/Dec/15 $$\mathrm{Given}\:\mathrm{a}\:\mathrm{set}\:\:{S}=\left\{{a}_{\mathrm{1}} ,\:…,\:{a}_{{n}} \right\} \\ $$$${a}_{{k}} \in\mathbb{Z} \\ $$$$ \\ $$$${a}_{\mathrm{1}} ={a},\:\:\:{a}_{{n}} ={a}_{{n}−\mathrm{1}} +\mathrm{1},\:\:\:{a}_{{n}} ={b} \\ $$$$…
Question Number 68591 by TawaTawa last updated on 14/Sep/19 Commented by kaivan.ahmadi last updated on 14/Sep/19 $$\mathrm{102}+\mathrm{2}{p}+\mathrm{3}{q}=\mathrm{0} \\ $$$$\mathrm{17}+\mathrm{3}{p}−\mathrm{4}{q}=\mathrm{0} \\ $$$$\Rightarrow \\ $$$$\begin{cases}{\mathrm{2}{p}+\mathrm{3}{q}=−\mathrm{102}}\\{\mathrm{3}{p}−\mathrm{4}{q}=−\mathrm{17}}\end{cases}\Rightarrow\begin{cases}{−\mathrm{6}{p}−\mathrm{9}{q}=\mathrm{306}}\\{\mathrm{6}{p}−\mathrm{8}{q}=−\mathrm{34}}\end{cases}\Rightarrow \\ $$$$−\mathrm{17}{q}=\mathrm{272}\Rightarrow{q}=−\mathrm{16}…
Question Number 134127 by bobhans last updated on 28/Feb/21 $$\:\mathrm{Given}\:\mid\mathrm{f}\left(\mathrm{x}\right)\mid\:=\:\mathrm{x}^{\mathrm{2}} \:\mathrm{for}\:−\mathrm{1}<\mathrm{x}<\mathrm{1} \\ $$$$\mathrm{find}\:\mathrm{f}\:'\left(\mathrm{0}\right). \\ $$ Commented by EDWIN88 last updated on 28/Feb/21 $$\mathrm{does}\:\mathrm{not}\:\mathrm{exist} \\ $$…
Question Number 68589 by peter frank last updated on 13/Sep/19 Answered by $@ty@m123 last updated on 14/Sep/19 $$\underset{{k}=\mathrm{2}} {\overset{{n}} {\sum}}\:\:\frac{\mathrm{1}}{{n}\left({n}+\mathrm{1}\right)} \\ $$$$=\underset{{k}=\mathrm{2}} {\overset{{n}} {\sum}}\:\left(\:\frac{\mathrm{1}}{{n}}−\frac{\mathrm{1}}{{n}+\mathrm{1}}\right) \\…
Question Number 3052 by Filup last updated on 04/Dec/15 $$\mathrm{Ever}\:\mathrm{used}\:\mathrm{Arrow}\:\mathrm{Notation}? \\ $$$$ \\ $$$$\mathrm{if}\:\mathrm{my}\:\mathrm{memory}\:\mathrm{is}\:\mathrm{correct}: \\ $$$$\mathrm{3}\uparrow\mathrm{3}=\mathrm{3}×\mathrm{3}×\mathrm{3}=\mathrm{3}^{\mathrm{3}} \\ $$$$\mathrm{3}\uparrow\uparrow\mathrm{3}=\left(\mathrm{3}\uparrow\mathrm{3}\right)\uparrow\mathrm{3}=\mathrm{3}^{\mathrm{3}} ×\mathrm{3}^{\mathrm{3}} ×\mathrm{3}^{\mathrm{3}} \\ $$$$\mathrm{etc}. \\ $$ Commented…
Question Number 134122 by Ahmed1hamouda last updated on 28/Feb/21 Answered by TheSupreme last updated on 28/Feb/21 $${x}=\mathrm{1}+\rho{cos}\left(\theta\right) \\ $$$${y}=\rho{sin}\left(\theta\right) \\ $$$${z}={z} \\ $$$${det}\left({J}\right)=\rho \\ $$$${E}=\left\{\left(\rho,\theta,{z}\right)\mid\mathrm{0}<\theta<\mathrm{2}\pi\:,\:\mathrm{0}<\rho<\mathrm{1},\:\mathrm{0}<{z}<\rho{sin}\theta\right\}…
Question Number 3048 by Syaka last updated on 03/Dec/15 $$\left.\mathrm{1}\right)\:\underset{{x}\:\rightarrow\:−\infty} {{lim}}\:\left(\mathrm{1}\:+\:\frac{\mathrm{1}}{{x}}\right)_{} ^{{x}\:} \:=\:? \\ $$$$ \\ $$$$ \\ $$ Answered by 123456 last updated on…
Question Number 134117 by ClarkeMelodyWenkeh last updated on 27/Feb/21 Answered by TheSupreme last updated on 28/Feb/21 $${A}=\mathrm{15} \\ $$$${B}=\mathrm{10} \\ $$$${A}\cup{B}={A}+{B}−{A}\cap{B}=\mathrm{20} \\ $$$${A}\cap{B}=\mathrm{15}+\mathrm{10}−\mathrm{20}=\mathrm{5} \\ $$$${p}\left({A}\cap{B}\right)=\frac{{A}\cap{B}}{{A}\cup{B}}=\frac{\mathrm{1}}{\mathrm{4}}…
Question Number 134116 by ClarkeMelodyWenkeh last updated on 27/Feb/21 Answered by EDWIN88 last updated on 27/Feb/21 $$\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{x}+\mathrm{3}\right)−\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{x}\right)=\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{8}\right) \\ $$$$\:\Leftrightarrow\:\frac{\mathrm{x}+\mathrm{3}}{\mathrm{x}}\:=\:\mathrm{8}\:,\:\mathrm{3}\:=\:\mathrm{7x}\:,\:\mathrm{x}\:=\:\frac{\mathrm{3}}{\mathrm{7}} \\ $$ Terms…
Question Number 3046 by Filup last updated on 03/Dec/15 $$\int_{\mathrm{0}} ^{\:{n}} {x}\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)\centerdot\centerdot\centerdot\left({x}+{n}\right){dx}=? \\ $$$$\left({x},\:{n}\right)\in\mathbb{R} \\ $$ Commented by Filup last updated on 04/Dec/15 $${x}\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)\centerdot\centerdot\centerdot\left({x}+{n}\right)=\frac{\left({x}+{n}\right)!}{\left({x}−\mathrm{1}\right)!} \\…