Question Number 140654 by muallim_riyoziyot last updated on 11/May/21 Answered by MJS_new last updated on 11/May/21 $$\mathrm{for}\:{x}\in\mathbb{R} \\ $$$$\sqrt[{\mathrm{3}}]{−{x}}=−\sqrt[{\mathrm{3}}]{{x}} \\ $$$$ \\ $$$$\left(\mathrm{2}\sqrt[{\mathrm{3}}]{\mathrm{2}{x}+\mathrm{1}}={x}^{\mathrm{3}} −\mathrm{1}\right)^{\mathrm{3}} \\…
Question Number 140650 by aurpeyz last updated on 10/May/21 $${find}\:{the}\:{integral}\:{of}\: \\ $$$$\frac{\mathrm{1}}{\pi}\underset{\mathrm{0}} {\overset{\pi} {\int}}{e}^{{ie}^{{ksin}^{\mathrm{2}} \emptyset} } {d}\emptyset \\ $$ Terms of Service Privacy Policy Contact:…
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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…
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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}}…