Question Number 23585 by Tinkutara last updated on 02/Nov/17 $$\mathrm{No}\:\mathrm{work}\:\mathrm{is}\:\mathrm{done}\:\mathrm{by}\:\mathrm{a}\:\mathrm{force}\:\mathrm{on}\:\mathrm{an}\:\mathrm{object}\:\mathrm{if} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{the}\:\mathrm{object}\:\mathrm{is}\:\mathrm{stationary}\:\mathrm{but}\:\mathrm{the} \\ $$$$\mathrm{point}\:\mathrm{of}\:\mathrm{application}\:\mathrm{of}\:\mathrm{the}\:\mathrm{force}\:\mathrm{moves} \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{object} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{the}\:\mathrm{object}\:\mathrm{moves}\:\mathrm{in}\:\mathrm{such}\:\mathrm{a}\:\mathrm{way} \\ $$$$\mathrm{that}\:\mathrm{the}\:\mathrm{point}\:\mathrm{of}\:\mathrm{application}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{force}\:\mathrm{remains}\:\mathrm{fixed} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{the}\:\mathrm{force}\:\mathrm{is}\:\mathrm{always}\:\mathrm{perpendicular}\:\mathrm{to} \\…
Question Number 23584 by A1B1C1D1 last updated on 02/Nov/17 Answered by FilupES last updated on 02/Nov/17 $$\underset{{x}\rightarrow\mathrm{0}^{\pm} } {\mathrm{lim}}\frac{\mathrm{ln}\left(\mathrm{3}+{x}\right)−\mathrm{ln}\left({x}\right)}{{x}}=\left(\underset{{x}\rightarrow\mathrm{0}^{\pm} } {\mathrm{lim}}\frac{\mathrm{1}}{{x}}\right)\left(\underset{{x}\rightarrow\mathrm{0}^{\pm} } {\mathrm{lim}}\left\{\mathrm{ln}\left(\mathrm{3}+{x}\right)−\mathrm{ln}\left({x}\right)\right\}\right) \\ $$$$\:…
Question Number 154652 by EDWIN88 last updated on 20/Sep/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{tan}\:\left({x}+\frac{\pi}{\mathrm{4}}\right)\mathrm{tan}\:\left(\mathrm{2}{x}+\frac{\pi}{\mathrm{4}}\right)\mathrm{tan}\:\left(\frac{\pi}{\mathrm{4}}−\mathrm{3}{x}\right)}{{x}^{\mathrm{3}} }=? \\ $$ Answered by bramlexs22 last updated on 20/Sep/21 Commented by mnjuly1970 last…
Question Number 154649 by mathdanisur last updated on 20/Sep/21 $$\mathrm{if}\:\:\mathrm{n}\:\in\:\mathbb{N}^{>\mathrm{2}} \:\:\mathrm{prove}\:\mathrm{that} \\ $$$$\left[\left(\sqrt[{\mathrm{3}}]{\mathrm{n}}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{n}\:+\:\mathrm{2}}\:\right)^{\mathrm{3}} \right]\:+\:\mathrm{1}\:=\:\mathrm{0}\:\left(\mathrm{mod}\:\mathrm{8}\right) \\ $$ Commented by MJS_new last updated on 20/Sep/21 $$\mathrm{just}\:\mathrm{a}\:\mathrm{try} \\…
Question Number 154648 by mathdanisur last updated on 20/Sep/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 154651 by mathdanisur last updated on 20/Sep/21 $$\mathrm{let}\:\mathrm{be}\:\:\boldsymbol{\mathrm{A}}\:=\:\begin{pmatrix}{\mathrm{1}}&{\mathrm{1}}\\{\mathrm{0}}&{\mathrm{1}}\end{pmatrix}\:\:;\:\:\boldsymbol{\mathrm{B}}\:=\:\begin{pmatrix}{\mathrm{1}}&{\mathrm{0}}\\{\mathrm{1}}&{\mathrm{1}}\end{pmatrix} \\ $$$$\mathrm{find}\:\:\boldsymbol{\Omega}\:=\:\mathrm{e}^{\boldsymbol{\mathrm{A}}} \:\centerdot\:\left(\mathrm{e}^{\boldsymbol{\mathrm{B}}} \right)^{−\mathrm{1}} \\ $$$$\left(\mathrm{e}^{\boldsymbol{\mathrm{A}}} \:-\:\mathrm{exponential}\:\mathrm{matrix}\right) \\ $$ Answered by TheHoneyCat last updated on…
Question Number 154647 by mathdanisur last updated on 20/Sep/21 $$\mathrm{f}\::\:\mathrm{Q}\:\rightarrow\:\mathrm{Q} \\ $$$$\mathrm{f}\left(\mathrm{x}\:+\:\mathrm{f}\left(\mathrm{y}\right)\right)\:=\:\mathrm{y}\:+\:\mathrm{f}\left(\mathrm{x}\right) \\ $$$$\forall\:\mathrm{x};\mathrm{y}\:\in\:\mathrm{Q} \\ $$ Answered by TheHoneyCat last updated on 20/Sep/21 $$\mathrm{I}\:\mathrm{demote}\:\mathrm{by}\:{f}^{{n}} \::\:{f}\circ…\circ{f}\:{n}\:\mathrm{times}…
Question Number 154641 by cesarL last updated on 20/Sep/21 $$\int\frac{\mathrm{1}−\sqrt{{x}}}{\:\sqrt{\mathrm{1}−{x}}}{dx} \\ $$ Answered by puissant last updated on 20/Sep/21 $${u}=\sqrt{\mathrm{1}−{x}}\rightarrow\:{u}^{\mathrm{2}} =\mathrm{1}−{x}\:\rightarrow\:{x}=\mathrm{1}−{u}^{\mathrm{2}} \\ $$$$\Rightarrow\:{dx}=−\mathrm{2}{udu}\: \\ $$$${I}=\int\frac{\mathrm{1}−\sqrt{\mathrm{1}−{u}^{\mathrm{2}}…
Question Number 154640 by Study last updated on 20/Sep/21 $$\underset{\mathrm{1}} {\overset{\mathrm{89}} {\sum}}{sin}^{\mathrm{2}} \left({x}\right)=? \\ $$ Answered by qaz last updated on 20/Sep/21 $$\underset{\mathrm{x}=\mathrm{1}°} {\overset{\mathrm{89}°} {\sum}}\mathrm{sin}\:^{\mathrm{2}}…
Question Number 89107 by unknown last updated on 15/Apr/20 Terms of Service Privacy Policy Contact: info@tinkutara.com