Question Number 127017 by mnjuly1970 last updated on 26/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{NICE}\:\:\:\:\:{CALCULUS}… \\ $$$$\:\:{prove}\:{that}\::: \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \:\left(\frac{{x}^{\mathrm{2}} {ln}\left(\pi{x}\right)}{\pi^{\pi{x}} }\right){dx} \\ $$$$\:\:=\frac{\mathrm{1}}{\left(\pi{ln}\left(\pi\right)\right)^{\mathrm{3}} }\left[\left(\mathrm{3}−\mathrm{2}\left(\gamma+{ln}\left({ln}\left(\pi\right)\right)\right)\right]\right. \\ $$ Answered by…
Question Number 192549 by cortano12 last updated on 20/May/23 $$\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mathrm{x}^{\mathrm{2}} \:\mathrm{tan}\:\left(\frac{\mathrm{sin}\:\pi\mathrm{x}}{\mathrm{2x}}\right)\:=? \\ $$ Answered by horsebrand11 last updated on 20/May/23 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{x}^{\mathrm{2}} \:\mathrm{tan}\:\left(\frac{\mathrm{sin}\:\pi{x}}{\mathrm{2}{x}}\right) \\…
Question Number 61479 by Tawa1 last updated on 03/Jun/19 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}:\:\:\:\:\:\:\:\frac{\mathrm{6}\sqrt{\mathrm{2x}}}{\mathrm{x}\:−\:\mathrm{1}}\:+\:\frac{\mathrm{5}\sqrt{\mathrm{x}\:−\:\mathrm{1}}}{\mathrm{2x}}\:\:\:=\:\:\mathrm{13} \\ $$ Commented by MJS last updated on 03/Jun/19 $$\mathrm{we}\:\mathrm{cannot}\:\mathrm{generally}\:\mathrm{solve}\:\mathrm{this}… \\ $$ Answered by ajfour…
Question Number 127012 by Algoritm last updated on 26/Dec/20 Answered by Olaf last updated on 26/Dec/20 $$\begin{cases}{{y}_{\mathrm{1}} '\:=\:{y}_{\mathrm{1}} +{y}_{\mathrm{2}} +\:{x}\:\left(\mathrm{1}\right)}\\{{y}_{\mathrm{2}} '\:=\:{y}_{\mathrm{1}} −\mathrm{2}{y}_{\mathrm{2}} +\mathrm{2}{x}\:\left(\mathrm{2}\right)}\end{cases} \\ $$$$\left(\mathrm{1}\right)\::\:{y}_{\mathrm{2}}…
Question Number 192550 by mokys last updated on 20/May/23 $${how}\:{can}\:{find}\:{the}\:{sum}\:\underset{{i}=\mathrm{1}} {\overset{{r}} {\sum}}\left(\mathrm{2}{v}_{{i}} +\mathrm{1}\right)\:? \\ $$ Answered by a.lgnaoui last updated on 20/May/23 $$\mathrm{S}_{\mathrm{i}} =\sum_{\mathrm{i}=\mathrm{1}} ^{\mathrm{i}=\mathrm{r}}…
Question Number 192545 by peter frank last updated on 20/May/23 Answered by BaliramKumar last updated on 20/May/23 $$\mathrm{plnx}+\mathrm{qlny}=\:\left(\mathrm{p}+\mathrm{q}\right)\mathrm{ln}\left(\mathrm{x}+\mathrm{y}\right) \\ $$$$\frac{\mathrm{p}}{\mathrm{x}}−\frac{\mathrm{p}+\mathrm{q}}{\mathrm{x}+\mathrm{y}}=\:\left\{\frac{\mathrm{p}+\mathrm{q}}{\mathrm{x}+\mathrm{y}}−\frac{\mathrm{q}}{\mathrm{y}}\right\}\frac{\mathrm{dy}}{\mathrm{dx}} \\ $$$$\frac{\mathrm{py}}{\mathrm{x}}\frac{−\mathrm{qx}}{}=\:\left\{\frac{\mathrm{py}−}{}\frac{\mathrm{qx}}{\mathrm{y}}\right\}\frac{\mathrm{dy}}{\mathrm{dx}} \\ $$$$\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{y}}{\mathrm{x}} \\…
Question Number 192544 by Mastermind last updated on 20/May/23 $$\mathrm{If}\:\mathrm{f}\left(\mathrm{t}\right)\:=\:\mathrm{2}\left(\mathrm{e}^{\mathrm{t}} \:−\:\mathrm{1}\right) \\ $$$$\left.\mathrm{a}\right)\:\mathrm{Does}\:\mathrm{f}\left(\mathrm{t}\right)\:\mathrm{exists}\:\mathrm{for}\:\mathrm{all}\:\mathrm{n}\:? \\ $$$$\left.\mathrm{b}\right)\:\mathrm{If}\:\mathrm{it}\:\mathrm{exist},\:\mathrm{does}\:\mathrm{it}\:\mathrm{converge}\:? \\ $$$$\left.\mathrm{c}\right)\:\mathrm{If}\:\mathrm{the}\:\mathrm{sequence}\:\mathrm{converge},\:\mathrm{does}\:\mathrm{the} \\ $$$$\mathrm{limit}\:\mathrm{converge}\:? \\ $$$$\left.\mathrm{d}\right)\:\mathrm{Is}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{uniques}\:? \\ $$ Commented by…
Question Number 127009 by BHOOPENDRA last updated on 26/Dec/20 $${f}\left({x},{y}\right)=\left\{\frac{\mathrm{2}{x}\left({x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\:\:\:\:,\left({x},{y}\right)\neq\left(\mathrm{0},\mathrm{0}\right)\right. \\ $$$$\left\{\mathrm{0}\:\:\:\:,\left({x},{y}\right)=\left(\mathrm{0},\mathrm{0}\right)\right. \\ $$$${check}\:{continuity} \\ $$ Answered by Olaf last updated…
Question Number 192541 by peter frank last updated on 20/May/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 127006 by liberty last updated on 26/Dec/20 $${Two}\:{pipes}\:{A}\:{and}\:{B}\:{together}\:{can}\:{fill}\: \\ $$$${a}\:{cistern}\:{in}\:\mathrm{5}\:{hours}.\:{Had}\:{they}\:{been}\:{opened} \\ $$$${separately},\:{then}\:{B}\:{would}\:{have}\:{taken}\: \\ $$$$\mathrm{6}\:{hours}\:{more}\:{than}\:{A}\:{to}\:{fill}\:{the}\:{cistern}. \\ $$$${How}\:{much}\:{time}\:{will}\:{be}\:{taken}\:{by}\:{A}\:{to}\:{fill} \\ $$$${the}\:{cistern}\:{separately}?\: \\ $$ Answered by bramlexs22…