Question Number 68595 by Abdo msup. last updated on 14/Sep/19 $${calculate}\:\:{A}_{\lambda} =\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{e}^{−\lambda{x}^{\mathrm{2}} } }{{x}^{\mathrm{4}} +\mathrm{1}}{dx}\:\:{with}\:\lambda>\mathrm{0}\:\:{and}\: \\ $$$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{A}_{\lambda} \:{d}\lambda \\ $$ Commented…
Question Number 3058 by pooran Yadav last updated on 04/Dec/15 $$\mathrm{2}{x}×\mathrm{3}{x} \\ $$ Answered by Rasheed Soomro last updated on 04/Dec/15 $$\left(\mathrm{2}×\mathrm{3}\right){x}^{\mathrm{2}} =\mathrm{6}{x}^{\mathrm{2}} \\ $$…
Question Number 68592 by Abdo msup. last updated on 14/Sep/19 $${find}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)^{\mathrm{3}} } \\ $$ Commented by Abdo msup. last updated on 16/Sep/19…
Question Number 68593 by Abdo msup. last updated on 14/Sep/19 $${calculate}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Commented by Abdo msup. last updated on 06/Oct/19…
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\}…