Question Number 151665 by Huy last updated on 22/Aug/21 $$\mathrm{prove}\:\mathrm{4arccot5}−\mathrm{arccot239}=\frac{\pi}{\mathrm{4}} \\ $$ Answered by puissant last updated on 22/Aug/21 $${tan}\left(\mathrm{4}{x}\right)=\frac{\mathrm{4}{tanx}−\mathrm{4}\left({tanx}\right)^{\mathrm{3}} }{\mathrm{1}−\mathrm{6}\left({tanx}\right)^{\mathrm{2}} +\left({tanx}\right)^{\mathrm{4}} } \\ $$$${tan}\left(\mathrm{4}{arctan}\frac{\mathrm{1}}{\mathrm{5}}\right)=\frac{\mathrm{120}}{\mathrm{119}}…
Question Number 86128 by M±th+et£s last updated on 27/Mar/20 $$\lfloor\mathrm{2}{x}−\frac{\mathrm{1}}{\mathrm{2}}\rfloor=\lfloor\mid{x}\mid−\frac{\mathrm{1}}{\mathrm{2}}\rfloor=\mathrm{2}{x}−\mathrm{2} \\ $$ Answered by mr W last updated on 27/Mar/20 $$\lfloor\mathrm{2}{x}−\frac{\mathrm{1}}{\mathrm{2}}\rfloor−\lfloor\mid{x}\mid−\frac{\mathrm{1}}{\mathrm{2}}\rfloor=\mathrm{2}{x}−\mathrm{2} \\ $$$$\lfloor\mathrm{2}{x}−\frac{\mathrm{1}}{\mathrm{2}}\rfloor−\lfloor\mid{x}\mid−\frac{\mathrm{1}}{\mathrm{2}}\rfloor=\mathrm{2}{x}−\mathrm{2}={n}=\begin{cases}{\mathrm{2}{k}}\\{\mathrm{2}{k}+\mathrm{1}}\end{cases} \\ $$$$\Rightarrow{x}=\frac{{n}}{\mathrm{2}}+\mathrm{1}=\begin{cases}{{k}+\mathrm{1}}\\{{k}+\frac{\mathrm{3}}{\mathrm{2}}}\end{cases}…
Question Number 86129 by oustmuchiya@gmail.com last updated on 27/Mar/20 $${Given}\:{that}\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\mathrm{8}\boldsymbol{\mathrm{x}}\:{and}\:\boldsymbol{\mathrm{g}}\left(\boldsymbol{\mathrm{x}}\right)=\frac{\mathrm{3}\boldsymbol{\mathrm{x}}−\mathrm{2}}{\mathrm{4}},\:{find} \\ $$$$\left(\mathrm{a}\right)\:\boldsymbol{\mathrm{f}}^{−\mathrm{1}} \left(\boldsymbol{\mathrm{x}}\right)\:\:\:\left(\mathrm{b}\right)\:{an}\:{expression}\:{for}\:\boldsymbol{{fg}}\left(\boldsymbol{\mathrm{x}}\right) \\ $$$$\left(\mathrm{c}\right)\:{value}\:{of}\:\boldsymbol{\mathrm{x}}\:{which}\:\boldsymbol{\mathrm{fg}}\left(\boldsymbol{\mathrm{x}}\right)=\mathrm{20}\: \\ $$ Commented by jagoll last updated on 27/Mar/20 $$\left.\mathrm{a}\right)\:\mathrm{f}^{−\mathrm{1}}…
Question Number 151660 by mathdanisur last updated on 22/Aug/21 Answered by Olaf_Thorendsen last updated on 22/Aug/21 $$\mathrm{ln}\left({e}+\mathrm{sin}{kx}\right)\:=\:\mathrm{1}+\mathrm{ln}\left(\mathrm{1}+\frac{\mathrm{sin}{kx}}{{e}}\right)\:\underset{\mathrm{0}} {\sim}\:\mathrm{1}+\frac{{kx}}{{e}} \\ $$$$\frac{\mathrm{1}−\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}\mathrm{ln}\left({e}+\mathrm{sin}{kx}\right)}{{x}}\:\underset{\mathrm{0}} {\sim}\:\frac{\mathrm{1}−\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}\left(\mathrm{1}+\frac{{kx}}{{e}}\right)}{{x}}\:\:\left(\mathrm{1}\right)…
Question Number 86120 by jagoll last updated on 27/Mar/20 $$\frac{\mathrm{dy}}{\mathrm{dx}}\:+\:\frac{\mathrm{sin}\:\mathrm{2y}}{\mathrm{x}}\:=\:\mathrm{x}^{\mathrm{3}} \:\mathrm{cos}\:^{\mathrm{2}} \:\mathrm{y} \\ $$ Commented by Prithwish Sen 1 last updated on 27/Mar/20 $${sir}\:{it}\:{is}\:{sin}\mathrm{2}{x}\:{not}\:{sin}\mathrm{2}{y}\:. \\…
Question Number 151652 by ArielVyny last updated on 22/Aug/21 $${faire}\:{la}\:{division}\:{de}\:\left(\mathrm{1}−{x}^{{n}} \right)\:{par}\:\left(\mathrm{1}−{x}\right) \\ $$ Answered by puissant last updated on 22/Aug/21 $$=\mathrm{1}+{x}+{x}^{\mathrm{2}} +….+{x}^{{n}−\mathrm{1}} \\ $$ Commented…
Question Number 86116 by Tony Lin last updated on 27/Mar/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{{tanx}}{{x}} \\ $$ Commented by john santu last updated on 27/Mar/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{sin}\:{x}}{{x}}\:×\:\frac{\mathrm{1}}{\mathrm{cos}\:{x}}\:=\:{DNE} \\…
Question Number 20581 by Tinkutara last updated on 28/Aug/17 $${The}\:{surface}\:{between}\:{wedge}\:{and}\:{block} \\ $$$${is}\:{rough}\:\left({Coefficient}\:{of}\:{friction}\:\mu\right). \\ $$$${Find}\:{out}\:{the}\:{range}\:{of}\:{F}\:{such}\:{that}, \\ $$$${there}\:{is}\:{no}\:{relative}\:{motion}\:{between} \\ $$$${wedge}\:{and}\:{block}.\:{The}\:{wedge}\:{can}\:{move} \\ $$$${freely}\:{on}\:{smooth}\:{ground}. \\ $$ Commented by Tinkutara…
Question Number 20579 by Tinkutara last updated on 28/Aug/17 $$\mathrm{A}\:\mathrm{1}\:\mathrm{kg}\:\mathrm{block}\:\mathrm{is}\:\mathrm{being}\:\mathrm{pushed}\:\mathrm{against}\:\mathrm{a} \\ $$$$\mathrm{wall}\:\mathrm{by}\:\mathrm{a}\:\mathrm{force}\:{F}\:=\:\mathrm{75}\:\mathrm{N}\:\mathrm{as}\:\mathrm{shown}\:\mathrm{in} \\ $$$$\mathrm{the}\:\mathrm{figure}.\:\mathrm{The}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{friction}\:\mathrm{is} \\ $$$$\mathrm{0}.\mathrm{25}.\:\mathrm{The}\:\mathrm{magnitude}\:\mathrm{of}\:\mathrm{acceleration}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{block}\:\mathrm{is} \\ $$ Commented by Tinkutara last updated…
Question Number 20578 by NECx last updated on 28/Aug/17 $$\:{Tinkutara}\:{and}\:\:{Ajfour}\:{please}\:{how} \\ $$$${do}\:{you}\:{do}\:{the}\:{following}\:{using} \\ $$$${lekh}\:{diagram}: \\ $$$$\left({i}\right){introduction}\:{of}\:{dotted}\:{lines} \\ $$$$\left({ii}\right){writing}\:{of}\:{letters} \\ $$$$\left({iii}\right){shading} \\ $$$$\left({iv}\right){putting}\:{colours}\:{in}\:{a}\:{diagram} \\ $$$$\left({v}\right){draw}\:{live}\:{figures}\:{like}\:{birds} \\…