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The-equation-of-the-curve-is-given-y-x-3-6-5x-2-2-6x-1-1-Determine-the-critical-points-2-Distinguish-between-these-points-3-Determine-the-Maximum-and-minimum-values-4-Determine-the-value-o

Question Number 169447 by Mastermind last updated on 30/Apr/22 $${The}\:{equation}\:{of}\:{the}\:{curve}\:{is}\:{given} \\ $$$${y}=\frac{{x}^{\mathrm{3}} }{\mathrm{6}}−\frac{\mathrm{5}{x}^{\mathrm{2}} }{\mathrm{2}}−\mathrm{6}{x}−\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{Determine}\:{the}\:{critical}\:{points} \\ $$$$\left.\mathrm{2}\right)\:{Distinguish}\:{between}\:{these}\:{points} \\ $$$$\left.\mathrm{3}\right)\:{Determine}\:{the}\:{Maximum}\:{and} \\ $$$${minimum}\:{values} \\ $$$$\left.\mathrm{4}\right)\:{Determine}\:{the}\:{value}\:{of}\:{x}\:{and}\:{y} \\…

Question-38373

Question Number 38373 by tanmay.chaudhury50@gmail.com last updated on 24/Jun/18 Commented by tanmay.chaudhury50@gmail.com last updated on 25/Jun/18 $${I}\left({a}\right)=\int_{\mathrm{0}} ^{\infty} \frac{{tan}^{−\mathrm{1}} \left({ax}\right)}{{x}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{dx} \\ $$$$\frac{{dI}\left({a}\right)}{{da}}=\int_{\mathrm{0}} ^{\infty} \frac{\partial}{\partial{a}}\frac{{tan}^{−\mathrm{1}}…

At-time-t-the-force-acting-on-a-particle-P-of-mass-2kg-is-2ti-4j-N-P-is-initially-at-rest-at-the-point-with-position-vector-i-2j-Find-a-the-velocity-of-P-when-t-2-b-the-position-vector-w

Question Number 38366 by Rio Mike last updated on 24/Jun/18 $${At}\:{time}\:{t},{the}\:{force}\:{acting}\:{on}\:{a}\:{particle} \\ $$$${P}\:{of}\:{mass}\:\mathrm{2}{kg}\:{is}\:\left(\mathrm{2}\boldsymbol{{ti}}\:+\:\mathrm{4}\boldsymbol{{j}}\right){N}.{P} \\ $$$${is}\:{initially}\:{at}\:{rest}\:{at}\:{the}\:{point}\:{with} \\ $$$${position}\:{vector}\:\left(\boldsymbol{{i}}\:+\:\mathrm{2}\boldsymbol{{j}}\right). \\ $$$${Find}: \\ $$$$\left.{a}\right)\:{the}\:{velocity}\:{of}\:{P}\:{when}\:{t}\:=\:\mathrm{2}. \\ $$$$\left.{b}\right)\:{the}\:{position}\:{vector}\:{when}\:{t}\:=\:\mathrm{2}. \\ $$…

A-particle-P-moves-on-a-straightline-from-a-fixed-point-O-and-the-distance-x-from-O-after-t-seconds-is-given-as-x-1-4-t-4-3-2-t-2-2t-Find-a-the-velocity-of-P-when-t-2-b-the-acce

Question Number 38365 by Rio Mike last updated on 24/Jun/18 $${A}\:{particle}\:{P}\:{moves}\:{on}\:{a}\:{straightline} \\ $$$${from}\:{a}\:{fixed}\:{point}\:{O}\:{and}\:{the}\:{distance} \\ $$$${x}\:{from}\:{O}\:{after}\:{t}\:{seconds}\:{is}\:{given}\:{as} \\ $$$$\:{x}\:=\:\frac{\mathrm{1}}{\mathrm{4}\:}\:{t}^{\mathrm{4}} \:−\:\frac{\mathrm{3}}{\mathrm{2}}\:{t}^{\mathrm{2}} \:+\:\mathrm{2}{t}. \\ $$$${Find}: \\ $$$$\left.{a}\right)\:{the}\:{velocity}\:{of}\:{P}\:{when}\:{t}\:=\:\mathrm{2}, \\ $$$$\left.{b}\right)\:{the}\:{acceleration}\:{of}\:{P}\:{when}\:{t}\:=\:\mathrm{2},…

solve-y-2-x-2-sin-pi-2-pi-2-

Question Number 103859 by 175mohamed last updated on 17/Jul/20 $$\:\:\: \\ $$$$\:\:\:\:\:\:{solve}\:: \\ $$$$\:\:\:\:\:\:{y}^{\mathrm{2}} \:+\:{x}^{\mathrm{2}} \:=\:−\mathrm{sin}\left(\theta\right)\:\:\:\:\:.,\:\:\:\:\frac{\pi}{\mathrm{2}}\geqslant\:\theta\geqslant−\frac{\pi}{\mathrm{2}} \\ $$ Answered by mathmax by abdo last updated…