Question Number 75100 by Rio Michael last updated on 07/Dec/19 $$\:{find}\:{the}\:{intervals}\:{cor}\:{which}\:{the}\:{function} \\ $$$${h}\left({x}\right)\:=\:{x}^{\mathrm{3}} −\mathrm{3}{x}\:{is} \\ $$$$\left.{a}\right)\:{strickly}\:{increasing} \\ $$$$\left.{b}\right)\:{strickly}\:{decreasing} \\ $$$$ \\ $$ Answered by mr…
Question Number 140628 by mohammad17 last updated on 10/May/21 $$\:{with}\:{out}\:{special}\:{function}\:{find} \\ $$$$ \\ $$$$\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{10}}} \sqrt{{tanx}}{dx}\:? \\ $$$$ \\ $$ Answered by Dwaipayan Shikari last…
Question Number 9530 by geovane10math last updated on 12/Dec/16 $$\mathrm{Why}\:\:{i}\:\ngtr\:\mathrm{0}\:\mathrm{and}\:{i}\:\nless\:\mathrm{0}\:???? \\ $$ Commented by geovane10math last updated on 14/Dec/16 $${why} \\ $$ Answered by nume1114…
Question Number 75059 by liki last updated on 06/Dec/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 140581 by bounhome last updated on 09/May/21 $${prove}\:\:\int{sec}^{\mathrm{2}} {xdx}={tanx} \\ $$ Answered by MJS_new last updated on 09/May/21 $$\mathrm{tan}\:{x}\:=\frac{\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}} \\ $$$$\frac{{d}}{{dx}}\left[\frac{{u}\left({x}\right)}{{v}\left({x}\right)}\right]=\frac{{u}'\left({x}\right){v}\left({x}\right)−{u}\left({x}\right){v}'\left({x}\right)}{\left({v}\left({x}\right)\right)^{\mathrm{2}} } \\…
Question Number 140576 by SOMEDAVONG last updated on 09/May/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\underset{\mathrm{n}=\mathrm{1}} {\overset{+\propto} {\sum}}\frac{\mathrm{2}^{\mathrm{n}} }{\mathrm{n}^{\mathrm{3}} }=? \\ $$ Answered by Dwaipayan Shikari last updated on 09/May/21 $${Li}_{\mathrm{3}}…
Question Number 75033 by naka3546 last updated on 06/Dec/19 $$\frac{\mathrm{4}}{\mathrm{11}}\:<\:\frac{{x}}{{y}}\:<\:\frac{\mathrm{3}}{\mathrm{8}} \\ $$$${x},\:{y}\:\:\in\:\:\mathbb{Z}^{+} \\ $$$${min}\:\left\{{x}+{y}\right\}\:\:=\:\:? \\ $$ Answered by mr W last updated on 06/Dec/19 $$\frac{\mathrm{4}}{\mathrm{11}}<\frac{{x}}{{y}}<\frac{\mathrm{3}}{\mathrm{8}}…
Question Number 140534 by SOMEDAVONG last updated on 09/May/21 Answered by EDWIN88 last updated on 09/May/21 $$\left(\mathrm{i}\right)\:=\:\frac{\mathrm{16x}−\mathrm{24}}{\left(\mathrm{x}−\mathrm{1}\right)\left(\mathrm{x}−\mathrm{3}\right)\left(\mathrm{x}+\mathrm{3}\right)}\:=\:\frac{\mathrm{a}}{\mathrm{x}−\mathrm{1}}+\frac{\mathrm{b}}{\mathrm{x}−\mathrm{3}}+\frac{\mathrm{c}}{\mathrm{x}+\mathrm{3}} \\ $$$$\mathrm{a}\:=\:\left[\frac{\mathrm{16x}−\mathrm{24}}{\left(\mathrm{x}−\mathrm{3}\right)\left(\mathrm{x}+\mathrm{3}\right)}\:\right]_{\mathrm{x}=\mathrm{1}} =\:\frac{−\mathrm{8}}{−\mathrm{8}}\:=\mathrm{1} \\ $$$$\mathrm{b}=\:\left[\frac{\mathrm{16x}−\mathrm{24}}{\left(\mathrm{x}−\mathrm{1}\right)\left(\mathrm{x}+\mathrm{3}\right)}\:\right]_{\mathrm{x}=\mathrm{3}} =\:\frac{\mathrm{48}−\mathrm{24}}{\mathrm{6}.\mathrm{2}}=\mathrm{2} \\ $$$$\mathrm{c}\:=\:\left[\frac{\mathrm{16x}−\mathrm{24}}{\left(\mathrm{x}−\mathrm{1}\right)\left(\mathrm{x}−\mathrm{3}\right)}\:\right]_{\mathrm{x}=−\mathrm{3}}…
Question Number 140529 by SOMEDAVONG last updated on 09/May/21 Answered by Rasheed.Sindhi last updated on 09/May/21 $$\frac{\mathrm{1}}{{x}^{\mathrm{2}} \left({x}+\mathrm{2}\right)}−\frac{\mathrm{5}}{\left({x}−\mathrm{2}\right)\left({x}+\mathrm{2}\right)}−\frac{\mathrm{4}}{{x}−\mathrm{2}} \\ $$$$=\frac{\mathrm{1}\left({x}−\mathrm{2}\right)−\mathrm{5}\left({x}^{\mathrm{2}} \right)−\mathrm{4}\left(\:{x}^{\mathrm{2}} \left({x}+\mathrm{2}\right)\:\right)}{{x}^{\mathrm{2}} \left({x}−\mathrm{2}\right)\left({x}+\mathrm{2}\right)} \\ $$$$=\frac{{x}−\mathrm{2}−\mathrm{5}{x}^{\mathrm{2}}…
Question Number 9458 by geovane10math last updated on 09/Dec/16 $$\mathrm{If}\:\mathrm{the}\:\mathrm{zeta}\:\mathrm{function}\:\mathrm{of}\:\mathrm{2}\:\mathrm{is} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\zeta}\left(\mathrm{2}\right)\:=\:\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\boldsymbol{{n}}^{\mathrm{2}} } \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\zeta}\left(\mathrm{2}\right)\:=\:\frac{\boldsymbol{\pi}^{\mathrm{2}} }{\mathrm{6}} \\ $$$$\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{infinite}\:\boldsymbol{\mathrm{rational}}\:\mathrm{numbers}, \\ $$$$\mathrm{why}\:\mathrm{converges}\:\mathrm{for}\:\frac{\boldsymbol{\pi}^{\mathrm{2}} }{\mathrm{6}},\:\mathrm{an}\:\boldsymbol{\mathrm{irrational}} \\ $$$$\mathrm{number}?…