Question Number 212171 by alcohol last updated on 04/Oct/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 212164 by mnjuly1970 last updated on 04/Oct/24 $$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\:\left(−\mathrm{1}\right)^{{n}} }{\mathrm{3}{n}+\mathrm{1}}\:−\:\mathrm{ln}\left(\sqrt[{\mathrm{3}}]{\mathrm{2}}\:\right)\:=\:? \\ $$$$\: \\ $$$$ \\ $$ Answered by…
Question Number 212160 by boblosh last updated on 04/Oct/24 Answered by A5T last updated on 04/Oct/24 $$\frac{{x}}{\mathrm{2}}+\mathrm{4}{y}=\mathrm{4}\Rightarrow{x}+\mathrm{8}{y}=\mathrm{8}…\left({i}\right) \\ $$$$\frac{{x}}{\mathrm{4}}−\frac{\mathrm{2}{y}}{\mathrm{3}}=\frac{\mathrm{2}}{\mathrm{3}}\Rightarrow\mathrm{3}{x}−\mathrm{8}{y}=\mathrm{8}…\left({ii}\right) \\ $$$$\begin{bmatrix}{\mathrm{1}}&{\mathrm{8}}\\{\mathrm{3}}&{−\mathrm{8}}\end{bmatrix}\begin{bmatrix}{{x}}\\{{y}}\end{bmatrix}=\begin{bmatrix}{\mathrm{8}}\\{\mathrm{8}}\end{bmatrix} \\ $$$${By}\:{Cramer}'{s}\:{rule}:\:{x}=\frac{\begin{vmatrix}{\mathrm{8}}&{\mathrm{8}}\\{\mathrm{8}}&{−\mathrm{8}}\end{vmatrix}}{\begin{vmatrix}{\mathrm{1}}&{\mathrm{8}}\\{\mathrm{3}}&{−\mathrm{8}}\end{vmatrix}}=\frac{−\mathrm{128}}{−\mathrm{32}}=\mathrm{4} \\ $$$${and}\:{y}=\frac{\begin{vmatrix}{\mathrm{1}}&{\mathrm{8}}\\{\mathrm{3}}&{\mathrm{8}}\end{vmatrix}}{\begin{vmatrix}{\mathrm{1}}&{\mathrm{8}}\\{\mathrm{3}}&{−\mathrm{8}}\end{vmatrix}}=\frac{−\mathrm{16}}{−\mathrm{32}}=\frac{\mathrm{1}}{\mathrm{2}}…
Question Number 212140 by mnjuly1970 last updated on 03/Oct/24 $$ \\ $$$$\:\mathrm{I}{f},\:\:\:\:\:{f}\left({x}\right)=−\:{x}^{\mathrm{2}} \:+\mathrm{4}{x}\:−\mathrm{3}\: \\ $$$$\:\:\:\:\: \\ $$$$,\:{g}\left({x}\right)=\:\begin{cases}{\:\sqrt{\mathrm{7}−{x}}\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{0}\leqslant{x}\:<\mathrm{7}}\\{\:\:\lfloor\:\mathrm{5}{x}\:\rfloor\:−\mathrm{5}{x}\:\:\:\:\:\:\:\:{x}\geqslant\mathrm{7}}\end{cases}\:\:\: \\ $$$$\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\Rightarrow\:\:\:\:\:\:{R}_{{fog}} \:=\:\left({a}\:,{b}\right]\:\: \\ $$$$\:\:\:\:\:\:\:{find}\:\:{the}\:{value}\:{of}\:\:\:{b}−{a} \\…
Question Number 212141 by MrGaster last updated on 03/Oct/24 $$ \\ $$$$\:\:\:\:\:\:\:\:\int\frac{\mathrm{cos}^{\mathrm{2}} {x}}{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}{dx}. \\ $$$$ \\ $$ Answered by BHOOPENDRA last updated on 03/Oct/24 $$\int\frac{\mathrm{cos}\:^{\mathrm{2}}…
Question Number 212136 by Subhi last updated on 03/Oct/24 $${what}\:{is}\:{the}\:{maximal}\:{number}\:{of}\:{consecutive}\:{natural} \\ $$$${numbers}\:{which}\:{are}\:{coprime}\:{with}\:{the} \\ $$$${sum}\:{of}\:{their}\:{divisors} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 212137 by MrGaster last updated on 03/Oct/24 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\sqrt[{{n}}]{{n}}−\mathrm{1}\right)\sqrt{{n}}=? \\ $$$$ \\ $$ Answered by Frix last updated on 03/Oct/24 $$\underset{{n}\rightarrow\infty}…
Question Number 212139 by mnjuly1970 last updated on 03/Oct/24 $$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\mathrm{I}_{{n}} \:=\:\int_{−\pi} ^{\:\pi} \frac{\:\mathrm{sin}\left({nx}\:\right)}{\left(\mathrm{1}\:+\:{e}^{{x}} \right)\mathrm{sin}{x}}\:{dx}\:=?\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\: \\ $$ Answered…
Question Number 212148 by boblosh last updated on 03/Oct/24 $$ \\ $$ Answered by Frix last updated on 03/Oct/24 $$\mathrm{42} \\ $$ Terms of Service…
Question Number 212146 by CrispyXYZ last updated on 03/Oct/24 $$\mathrm{Find}\:\mathrm{maximum}\:\mathrm{without}\:\mathrm{derivative} \\ $$$${x}\left(\mathrm{6}−{x}\right)\left({x}−\mathrm{3}\right)^{\mathrm{2}} \:\left(\mathrm{3}<{x}<\mathrm{6}\right) \\ $$ Answered by Frix last updated on 03/Oct/24 $$\mathrm{Let}\:{x}=\mathrm{3}+\mathrm{3sin}\:{t} \\ $$$${x}\left(\mathrm{6}−{x}\right)\left({x}−\mathrm{3}\right)^{\mathrm{2}}…