Question Number 28479 by naka3546 last updated on 26/Jan/18 Answered by ajfour last updated on 26/Jan/18 $$\mathrm{1}+\frac{\pi}{\mathrm{3}}−\sqrt{\mathrm{3}} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 28456 by mondodotto@gmail.com last updated on 26/Jan/18 Commented by Tinkutara last updated on 26/Jan/18 5 Answered by Rasheed.Sindhi last updated on 26/Jan/18 $$\mathrm{f}\left(\mathrm{2}\right)=\mathrm{5},\mathrm{f}\left(\mathrm{3}\right)=\mathrm{4},\mathrm{g}\left(\mathrm{2}\right)=\mathrm{5},\mathrm{g}\left(\mathrm{3}\right)=\mathrm{2},\mathrm{g}\left(\mathrm{4}\right)=\mathrm{1}…
Question Number 159497 by naka3546 last updated on 17/Nov/21 $${Prove}\:\:{that}\:\: \\ $$$$\:\:\:\:\:\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{4}}\:+\:\frac{\mathrm{1}}{\mathrm{9}}\:+\:\ldots+\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\:\:<\:\:\mathrm{2} \\ $$$${for}\:\:{n}\:\in\:\:\mathbb{N}\:\:. \\ $$ Commented by mr W last updated on 18/Nov/21…
Question Number 159491 by akolade last updated on 17/Nov/21 Answered by Tokugami last updated on 18/Nov/21 $$\int_{\mathrm{0}} ^{\:\frac{{d}}{{dx}}\int_{\mathrm{0}} ^{\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{e}^{−{x}} \underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{x}^{{k}} }{{k}!}} \pi\:{dt}}…
Question Number 159480 by ZiYangLee last updated on 17/Nov/21 Commented by bobhans last updated on 18/Nov/21 $$\:\begin{cases}{\mathrm{z}=\mathrm{cos}\:\theta\:+\mathrm{i}\:\mathrm{sin}\:\theta}\\{\frac{\mathrm{1}}{\mathrm{z}}=\mathrm{cos}\:\theta−\mathrm{i}\:\mathrm{sin}\:\theta}\end{cases}\:;\:\begin{cases}{\mathrm{z}^{\mathrm{6}} =\mathrm{cos}\:\mathrm{6}\theta+\mathrm{i}\:\mathrm{sin}\:\mathrm{6}\theta}\\{\frac{\mathrm{1}}{\mathrm{z}^{\mathrm{6}} }=\mathrm{cos}\:\mathrm{6}\theta−\mathrm{i}\:\mathrm{sin}\:\mathrm{6}\theta}\end{cases} \\ $$$$\:\mathrm{z}^{\mathrm{6}} +\frac{\mathrm{1}}{\mathrm{z}^{\mathrm{6}} }\:=\:\mathrm{2cos}\:\mathrm{6}\theta \\ $$$$\Rightarrow\left(\mathrm{z}^{\mathrm{3}}…
Question Number 159469 by 0731619 last updated on 17/Nov/21 Commented by cortano last updated on 17/Nov/21 $$\:\sqrt{{x}}\:=\:{u}\:{and}\:\sqrt{{y}}\:=\:{v}\: \\ $$$$\:\begin{cases}{{u}^{\mathrm{3}} +{v}^{\mathrm{3}} \:=\:\mathrm{35}}\\{{u}^{\mathrm{2}} \:{v}+\:{uv}^{\mathrm{2}} \:=\:\mathrm{30}}\end{cases} \\ $$$$\:\begin{cases}{{u}^{\mathrm{3}}…
Question Number 159433 by joki last updated on 17/Nov/21 $$\frac{\mathrm{5x}^{\mathrm{2}} −\mathrm{15x}−\mathrm{11}}{\left(\mathrm{x}+\mathrm{1}\right)\left(\mathrm{x}−\mathrm{2}\right)^{\mathrm{2}} }\:\mathrm{fractio}\:\mathrm{partil} \\ $$$$ \\ $$ Commented by cortano last updated on 17/Nov/21 $$\:\frac{\mathrm{5}{x}^{\mathrm{2}} −\mathrm{15}{x}−\mathrm{11}}{\left({x}+\mathrm{1}\right)\left({x}−\mathrm{2}\right)^{\mathrm{2}}…
Question Number 159428 by mkam last updated on 16/Nov/21 $$\frac{{dy}}{{dx}}={cos}\left({x}+{y}\right)+{sin}\left({x}+{y}\right) \\ $$ Answered by mr W last updated on 16/Nov/21 $${let}\:{u}={x}+{y} \\ $$$$\frac{{du}}{{dx}}=\mathrm{1}+\frac{{dy}}{{dx}} \\ $$$$\frac{{du}}{{dx}}−\mathrm{1}=\mathrm{cos}\:{u}+\mathrm{sin}\:{u}=\sqrt{\mathrm{2}}\mathrm{sin}\:\left({u}+\frac{\pi}{\mathrm{4}}\right)…
Question Number 159431 by ghakhan88 last updated on 16/Nov/21 Answered by mr W last updated on 17/Nov/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\int_{\mathrm{0}} ^{{x}} \frac{{t}^{\mu−\mathrm{1}} }{{x}^{\mu} }{u}\left({t}\right){dt} \\ $$$$=\underset{{x}\rightarrow\mathrm{0}}…
Question Number 93843 by naka3546 last updated on 15/May/20 $${Use}\:\:{Horner}\:\:{to}\:\:{solve}\:{it}\:. \\ $$$$\:\:\left({a}^{\mathrm{2}} −\mathrm{5}{ab}−\mathrm{3}{b}^{\mathrm{2}} \right)\::\:\left({a}−{b}\right) \\ $$$${find}\:\:{the}\:\:{remainder}\:\:. \\ $$ Answered by i jagooll last updated on…