Question Number 171032 by Mastermind last updated on 06/Jun/22 $${Find}\:{the}\:{domain}\:{and}\:{range}\:{of}\:{the} \\ $$$${function},\:{f}\left({x}\right)=\frac{{x}^{\mathrm{2}} +\mathrm{2}}{\mathrm{2}{x}+\mathrm{1}} \\ $$$$ \\ $$$${Mastermind} \\ $$ Answered by cortano1 last updated on…
Question Number 171025 by Mastermind last updated on 06/Jun/22 Answered by greougoury555 last updated on 06/Jun/22 $$\left(\mathrm{1}\right)\:{x}\geqslant−\mathrm{3}\Rightarrow\frac{\mathrm{2}{x}+\mathrm{3}−{x}−\mathrm{2}}{{x}+\mathrm{2}}\:>\mathrm{0} \\ $$$$\:\Rightarrow\frac{{x}+\mathrm{1}}{{x}+\mathrm{2}}\:>\mathrm{0}\:;\:{x}<−\mathrm{2}\:\cup\:{x}>−\mathrm{1}\: \\ $$$$\:\therefore\:{solution}\::\:\left[−\mathrm{3},−\mathrm{2}\right)\:\cup\left(−\mathrm{1},\infty\right) \\ $$$$\left(\mathrm{2}\right)\:{x}<−\mathrm{3}\Rightarrow\frac{−\mathrm{3}−{x}−\mathrm{2}}{{x}+\mathrm{2}}\:>\mathrm{0} \\ $$$$\Rightarrow\:\frac{−{x}−\mathrm{5}}{{x}+\mathrm{2}}\:>\mathrm{0}\:;\:\frac{{x}+\mathrm{5}}{{x}+\mathrm{2}}\:<\mathrm{0}…
Question Number 105488 by 175mohamed last updated on 29/Jul/20 $${if}\:{y}\:=\:{cos}\left({x}^{\mathrm{2}} \right)\:\:\:\:\:\:{then}\: \\ $$$$\:\:\:\:\:\:{y}^{\left({n}\right)} \:=\:……… \\ $$ Answered by mathmax by abdo last updated on 29/Jul/20…
Question Number 171009 by Mastermind last updated on 06/Jun/22 $${Find}\:{the}\:{inverse},\:{y}^{−\mathrm{1}} \:{of}\:{the}\:{function} \\ $$$${y}={x}^{\mathrm{3}} +\mathrm{4}. \\ $$$$ \\ $$$${Mastermind} \\ $$ Answered by a.lgnaoui last updated…
Question Number 171008 by Mastermind last updated on 06/Jun/22 $${Find}\:{the}\:{maximum}\:{and}\:{minimum} \\ $$$${values}\:{of}\:{h}\left({x}\right)=\frac{\mathrm{4}}{\mathrm{3}}{x}^{\mathrm{3}} +\frac{\mathrm{9}}{\mathrm{2}}{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{8}. \\ $$$$ \\ $$$${Mastermind} \\ $$ Commented by mr W last…
Question Number 171005 by Mastermind last updated on 06/Jun/22 $${The}\:{distance}\:{S}\:{metre}\:{travelled}\:{in}\:{time} \\ $$$${t}\:{seconds}\:{by}\:{an}\:{object}\:{released}\:{from} \\ $$$${rest}\:{and}\:{allow}\:{to}\:{fall}\:{freely}\:{under}\:{the} \\ $$$${force}\:{of}\:{gravity}\:{is}\:{given}\:{by}\:{s}\left({t}\right)=\mathrm{4}.\mathrm{5}{t}^{\mathrm{2}} . \\ $$$${find}\: \\ $$$$\left.{a}\right)\:{the}\:{average}\:{speed}\:{of}\:{the}\:{object} \\ $$$${during}\:{the}\:{time}\:{interval}\:{from}\:\mathrm{2}\:{to} \\ $$$$\mathrm{2}.\mathrm{5}\:{seconds}.…
Question Number 171006 by Mastermind last updated on 06/Jun/22 $${Find}\:{the}\:{area}\:{enclosed}\:{by}\:{the}\:{curve} \\ $$$${y}=\mathrm{4}−\mathrm{3}{x}^{\mathrm{2}} \:{and}\:{the}\:{x}−{axis}\:{between} \\ $$$${x}_{\mathrm{1}} =−\mathrm{1}\:{and}\:{x}_{\mathrm{2}} =\mathrm{1}. \\ $$$$ \\ $$$${Mastermind} \\ $$ Commented by…
Question Number 170997 by Mastermind last updated on 06/Jun/22 $${Find}\:{the}\:{equation}\:{of}\:{the}\:{tangent}\:{to}\:{the} \\ $$$${curve}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{6}{y}−\mathrm{12}=\mathrm{0}\:{at}\:{the} \\ $$$${point}\:\left(\mathrm{2},\:\mathrm{3}\right). \\ $$$$ \\ $$$${Mastermind} \\ $$ Answered by depressiveshrek…
Question Number 170996 by Mastermind last updated on 06/Jun/22 $${Find}\:{the}\:{volume}\:{of}\:{the}\:{solid}\:{obtained} \\ $$$${by}\:{rotating}\:{about}\:{x}−{axis}\:{of}\:{the}\:{curve} \\ $$$${y}=\sqrt{{x}}\:{on}\:{the}\:{interval}\:\left[\mathrm{0},\:\mathrm{2}\right]. \\ $$$$ \\ $$$${Mastermind} \\ $$ Answered by mr W last…
Question Number 170995 by Mastermind last updated on 05/Jun/22 $${Approximate}\:{sin}\mathrm{46}°\:{by}\:“{differentials}'' \\ $$$$ \\ $$$${Mastermind} \\ $$ Commented by mr W last updated on 06/Jun/22 $$\mathrm{sin}\:\mathrm{46}°=\mathrm{sin}\:\left(\frac{\pi}{\mathrm{4}}+\frac{\pi}{\mathrm{180}}\right)…