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f-x-arctan-1-x-1-x-ask-f-2023-0-

Question Number 212177 by MrGaster last updated on 05/Oct/24 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{f}\left({x}\right)=\mathrm{arctan}\left(\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}\right)=? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{ask}:{f}^{\mathrm{2023}} \left(\mathrm{0}\right) \\ $$ Answered by a.lgnaoui last updated on 05/Oct/24 $$\mathrm{f}\left(\mathrm{0}\right)=\frac{\pi}{\mathrm{4}}\Rightarrow\:\:\:\mathrm{f}^{\mathrm{2023}} \left(\mathrm{0}\right)=\frac{\pi^{\mathrm{2023}} }{\mathrm{4}^{\mathrm{2023}}…

Question-212159

Question Number 212159 by boblosh last updated on 04/Oct/24 Answered by Rasheed.Sindhi last updated on 04/Oct/24 $$\begin{bmatrix}{\:\:\:\:\:\mathrm{2}}&{\:\:\:\:\mathrm{3}}\\{−\mathrm{1}}&{−\mathrm{1}}\end{bmatrix}+{a}\begin{bmatrix}{\mathrm{2}}&{\mathrm{1}}\\{\mathrm{0}}&{\mathrm{4}}\end{bmatrix}=\begin{bmatrix}{\mathrm{8}}&{{b}}\\{{c}}&{{d}}\end{bmatrix} \\ $$$$\begin{bmatrix}{\mathrm{2}{a}+\mathrm{2}}&{{a}+\mathrm{3}}\\{\mathrm{0}{a}−\mathrm{1}}&{\mathrm{4}{a}−\mathrm{1}}\end{bmatrix}=\begin{bmatrix}{\mathrm{8}}&{{b}}\\{{c}}&{{d}}\end{bmatrix} \\ $$$$\mathrm{2}{a}+\mathrm{2}=\mathrm{8}\Rightarrow{a}=\mathrm{3} \\ $$$${c}=−\mathrm{1} \\ $$$${b}={a}+\mathrm{3}=\mathrm{3}+\mathrm{3}=\mathrm{6}…

Question-212160

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}}…

lim-n-n-1-n-1-n-

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}…

Find-maximum-without-derivative-x-6-x-x-3-2-3-lt-x-lt-6-

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}}…

Question-212130

Question Number 212130 by Ismoiljon_008 last updated on 02/Oct/24 $$\:\:\:\: \\ $$ Answered by a.lgnaoui last updated on 03/Oct/24 $$\:\:\:\:\frac{\mathrm{AD}}{\mathrm{BC}}=\mathrm{2},\mathrm{48}\:\left(\mathrm{detail}\:\mathrm{en}\:\mathrm{commentaire}\right) \\ $$ Commented by a.lgnaoui…