Question Number 136138 by bramlexs22 last updated on 19/Mar/21 $${What}\:{is}\:{max}\:{and}\:{min}\:{value} \\ $$$${of}\:{y}=\mathrm{4}−{x}^{\mathrm{2}} −\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\:? \\ $$ Answered by ajfour last updated on 19/Mar/21 $${let}\:\:\mathrm{1}−{x}^{\mathrm{2}} ={s}\geqslant\mathrm{0}…
Question Number 70582 by Raphael last updated on 05/Oct/19 $$\mathrm{Given}\:\mathrm{that}\:\mathrm{y}=\frac{\mathrm{4}}{\:\sqrt{\left(\mathrm{x}^{\mathrm{3}} +\mathrm{1}\right)}}\:\mathrm{show}\:\mathrm{that}\:\mathrm{2}\left(\mathrm{x}^{\mathrm{3}} +\mathrm{1}\right)\frac{\mathrm{dy}}{\mathrm{dx}}=−\mathrm{3x}^{\mathrm{2}} \mathrm{y}. \\ $$ Commented by kaivan.ahmadi last updated on 05/Oct/19 $$\mathrm{2}\left({x}^{\mathrm{3}} +\mathrm{1}\right)×\frac{−\frac{\mathrm{4}×\mathrm{3}{x}^{\mathrm{2}} }{\mathrm{2}\sqrt{{x}^{\mathrm{3}}…
Question Number 70583 by Raphael last updated on 05/Oct/19 $$\mathrm{Given}\:\mathrm{that}\:\mathrm{y}=\frac{\mathrm{4}}{\:\sqrt{\left(\mathrm{x}^{\mathrm{3}} +\mathrm{1}\right)}}\:\mathrm{show}\:\mathrm{that}\:\mathrm{2}\left(\mathrm{x}^{\mathrm{3}} +\mathrm{1}\right)\frac{\mathrm{dy}}{\mathrm{dx}}=−\mathrm{3x}^{\mathrm{2}} \mathrm{y}. \\ $$ Answered by MJS last updated on 05/Oct/19 $${dy}=−\frac{\mathrm{6}{x}^{\mathrm{2}} }{\left({x}^{\mathrm{3}} +\mathrm{1}\right)^{\mathrm{3}/\mathrm{2}}…
Question Number 4993 by love math last updated on 29/Mar/16 $${f}\left({x}\right)=\frac{{x}\:{ln}\:{x}}{\mathrm{1}+\:{e}^{{x}} } \\ $$$$ \\ $$$${f}\:'\left({x}\right)\:−\:? \\ $$ Answered by FilupSmith last updated on 30/Mar/16…
Question Number 4992 by love math last updated on 29/Mar/16 $${f}\left({x}\right)=\mathrm{2}{x}\:{e}^{{x}} \\ $$$${f}\:'\left({x}\right)\:−? \\ $$ Answered by FilupSmith last updated on 29/Mar/16 $${f}\left({x}\right)={uv} \\ $$$${f}\left({x}\right)={uv}'+{u}'{v}…
Question Number 136006 by liberty last updated on 17/Mar/21 $$ \\ $$What are the dimensions of the rectangle of maximum area that can be inscribed…
Question Number 4925 by sanusihammed last updated on 22/Mar/16 $${If}\:{y}\:=\:\left({secx}\:+\:{tanx}\right)^{{p}} \:.\:{where}\:{p}\:{is}\:{a}\:{constant}\: \\ $$$${prove}\:{that}\:\:\:\:{cosx}\:{dy}/{dx}\:−\:{py}\:=\:\mathrm{0} \\ $$$$ \\ $$ Answered by prakash jain last updated on 22/Mar/16…
Question Number 135944 by mnjuly1970 last updated on 17/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:…..{nice}\:\:{calculus}… \\ $$$$\:\:\:{prove}\:{that}: \\ $$$$\:\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(\sqrt{\mathrm{2}}\:−\mathrm{1}\right)^{{n}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} }=\frac{\pi^{\mathrm{2}} }{\mathrm{8}}−\frac{\mathrm{1}}{\mathrm{2}}{ln}^{\mathrm{2}} \left(\mathrm{1}+\sqrt{\mathrm{2}}\:\right)… \\ $$$$\:\:\:\:…………….\checkmark \\ $$ Answered…
Question Number 135935 by Engr_Jidda last updated on 17/Mar/21 $${If}\:\:{v}={r}^{{m}} \:{where}\:{r}=\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \:}\:,\:{show}\:{that} \\ $$$$\frac{\partial^{\mathrm{2}} {v}}{\partial{x}^{\mathrm{2}} }+\frac{\partial^{\mathrm{2}} {v}}{\partial{y}^{\mathrm{2}} }+\frac{\partial^{\mathrm{2}} {v}}{\partial{z}^{\mathrm{2}} }={m}\left({m}−\mathrm{1}\right){r}^{{m}−\mathrm{2}} \\ $$ Answered…
Question Number 135929 by Engr_Jidda last updated on 17/Mar/21 $${Verify}\:{that}\:{the}\:{following}\:{functions}\:{satisfies} \\ $$$${the}\:{mean}\:{value}\:{theorem}. \\ $$$$\left(\mathrm{1}\right)\:\:\:{f}\left({x}\right)\:=\frac{{x}}{{x}^{\mathrm{2}} −{x}}\:\:\:{at}\:\left[−\mathrm{2},−\mathrm{1}\right] \\ $$$$\left(\mathrm{2}\right)\:\:{f}\left({x}\right)={x}^{\mathrm{3}} −\mathrm{4}{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{4}\:\:\:{at}\left[−\mathrm{2},\mathrm{2}\right] \\ $$ Terms of Service Privacy…