Question Number 118887 by rexfordattacudjoe last updated on 20/Oct/20 Answered by benjo_mathlover last updated on 20/Oct/20 $$\:{f}\:'\left({x}\right)\:=\:\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{{x}+{h}}\:−\sqrt{{x}}}{{h}} \\ $$$$\:=\:\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}+{h}−{x}}{{h}}\:×\:\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}}{\:\sqrt{{x}+{h}}\:+\:\sqrt{{x}}\:} \\ $$$$=\:\mathrm{1}×\frac{\mathrm{1}}{\mathrm{2}\sqrt{{x}}}\:=\:\frac{\mathrm{1}}{\mathrm{2}\sqrt{{x}}} \\…
Question Number 118701 by bemath last updated on 19/Oct/20 $${What}\:{is}\:{maximum}\:{value} \\ $$$$\:{x}^{\mathrm{3}} {y}^{\mathrm{3}} \:+\mathrm{3}{xy}\:{when}\:{x}+{y}\:=\:\mathrm{8}? \\ $$ Commented by PRITHWISH SEN 2 last updated on 19/Oct/20…
Question Number 118665 by rexfordattacudjoe last updated on 19/Oct/20 Answered by bemath last updated on 19/Oct/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 184175 by mnjuly1970 last updated on 03/Jan/23 Answered by SEKRET last updated on 03/Jan/23 $$ \\ $$ Commented by SEKRET last updated on…
Question Number 118612 by rexfordattacudjoe last updated on 18/Oct/20 Answered by 1549442205PVT last updated on 18/Oct/20 $$\mathrm{y}=\mathrm{0}.\mathrm{4x}^{\mathrm{2}} −\mathrm{36x}+\mathrm{1000}= \\ $$$$\frac{\mathrm{4}}{\mathrm{10}}\left(\mathrm{x}^{\mathrm{2}} −\mathrm{90x}+\mathrm{2500}\right)=\frac{\mathrm{2}}{\mathrm{5}}\left[\left(\mathrm{x}−\mathrm{45}\right)^{\mathrm{2}} +\mathrm{475}\right] \\ $$$$\geqslant\frac{\mathrm{2}.\mathrm{475}}{\mathrm{5}}=\mathrm{190} \\…
Question Number 118570 by rexfordattacudjoe last updated on 18/Oct/20 $${Find}\:{the}\:{dimensions}\:{of}\:{the} \\ $$$${largest}\:{rectangular}\:{garden}\:{that} \\ $$$${can}\:{be}\:{enclosed}\:{by}\:\mathrm{80}{m}\:{of} \\ $$$${fencing} \\ $$ Answered by TANMAY PANACEA last updated on…
Question Number 184040 by pete last updated on 02/Jan/23 $$\mathrm{Use}\:\mathrm{implicit}\:\mathrm{differentiation}\:\mathrm{to}\:\mathrm{find}\:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} } \\ $$$$\mathrm{for}\:\mathrm{sin}{y}\:=\:{x} \\ $$ Answered by cortano2 last updated on 02/Jan/23 $${y}'\mathrm{cos}\:{y}=\mathrm{1} \\…
Question Number 52945 by Tawa1 last updated on 15/Jan/19 Commented by maxmathsup by imad last updated on 15/Jan/19 $$\left.\mathrm{3}\right)\:{let}\:{A}\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{x}\:{ln}^{\mathrm{2}} \left({x}\right)}{{e}^{{x}} −\mathrm{1}}\:{dx}\:\Rightarrow{A}\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{x}\:{e}^{−{x}}…
Question Number 118364 by mnjuly1970 last updated on 17/Oct/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:…{ordinary}\:{differential}\:{equation}… \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:{y}''\:−{xy}'+{y}=\mathrm{0} \\ $$$$\:\:\:\:{general}\:{solution}\:::=?? \\ $$$$\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:.{m}.{n}.\mathrm{1970}. \\ $$$$ \\ $$ Answered…
Question Number 52820 by 33 last updated on 13/Jan/19 $${y}\:=\:{log}\left\{\sqrt{{x}}\:+\frac{\mathrm{1}}{\:\sqrt{{x}}\:\:\:}\right\}^{\mathrm{2}} \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$${show}\:{that} \\ $$$${x}\left({x}+\mathrm{1}\right)^{\mathrm{2}} {y}_{\mathrm{2}} \:+\:\left({x}+\mathrm{1}\right)^{\mathrm{2}} {y}_{\mathrm{1}} \:=\:\mathrm{2} \\ $$ Answered by tanmay.chaudhury50@gmail.com last…