Question Number 228464 by fantastic2 last updated on 17/Apr/26 $$\int{x}\mathrm{sin}^{−\mathrm{1}} {xdx} \\ $$ Commented by fantastic2 last updated on 18/Apr/26 $$\int{udv}={uv}−\int{vdu} \\ $$$${here}\:{u}=\mathrm{sin}^{−\mathrm{1}} {x}\Rightarrow{du}=\frac{{dx}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}…
Question Number 228440 by fantastic2 last updated on 14/Apr/26 $$\mathrm{3}^{{x}} +\mathrm{9}^{{x}} +\mathrm{27}^{{x}} =\mathrm{14} \\ $$ Answered by Lara2440 last updated on 15/Apr/26 $$\mathrm{3}^{{x}} \:\overset{\mathrm{Substitution}} {=}{u}\:,\:{u}>\mathrm{0}…
Question Number 228430 by Kassista last updated on 13/Apr/26 Answered by TonyCWX last updated on 16/Apr/26 $$\mathrm{det}\left({g}\left({x}\right)\right)\:=\:\mathrm{64sin}\left({x}\right)\mathrm{ln}\left({x}\right)−\:\mathrm{2}^{\mathrm{cos}\left({x}\right)\:+\:\mathrm{3}} \left[\mathrm{48}\left({x}^{\mathrm{2}} \:−\:\mathrm{3}{x}\:+\:\mathrm{5}\right)\right] \\ $$$${M}_{{g}} \left({x}\right)\:=\:\mathrm{64cos}\left({x}\right)\mathrm{ln}\left({x}\right)\:+\:\frac{\mathrm{64sin}\left({x}\right)}{{x}}\:−\:\mathrm{ln}\left(\mathrm{2}\right)\left[−\mathrm{sin}\left({x}\right)\right]\mathrm{2}^{\mathrm{cos}\left({x}\right)\:+\:\mathrm{3}} \left[\mathrm{48}\left({x}^{\mathrm{2}} \:−\:\mathrm{3}{x}\:+\:\mathrm{5}\right)\right]\:−\:\mathrm{2}^{\mathrm{cos}\left({x}\right)\:+\:\mathrm{3}} \left[\mathrm{48}\left(\mathrm{2}{x}\:−\:\mathrm{3}\right)\right]…
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Question Number 228335 by fantastic2 last updated on 07/Apr/26 $${x}+\frac{\mathrm{1}}{{x}}=\sqrt{\mathrm{3}} \\ $$$${x}^{\mathrm{30}} +{x}^{\mathrm{24}} +{x}^{\mathrm{18}} +{x}^{\mathrm{12}} +{x}^{\mathrm{6}} +\mathrm{1}=? \\ $$ Answered by AgniMath last updated on…
Question Number 228331 by fantastic2 last updated on 07/Apr/26 $${x}=\frac{\sqrt{\mathrm{2}}+\mathrm{1}}{\:\sqrt{\mathrm{2}}−\mathrm{1}}\:\&{x}−{y}=\mathrm{4}\sqrt{\mathrm{2}} \\ $$$${x}^{\mathrm{4}} +{y}^{\mathrm{4}} =? \\ $$ Answered by TonyCWX last updated on 07/Apr/26 $${x}\:=\:\frac{\sqrt{\mathrm{2}}\:+\:\mathrm{1}}{\:\sqrt{\mathrm{2}}\:−\:\mathrm{1}}\:=\:\frac{\mathrm{3}\:+\:\mathrm{2}\sqrt{\mathrm{2}}}{\mathrm{2}\:−\:\mathrm{1}}\:=\:\mathrm{3}\:+\:\mathrm{2}\sqrt{\mathrm{2}} \\…
Question Number 228339 by absee last updated on 07/Apr/26 Answered by Frix last updated on 08/Apr/26 $$\mathrm{You}\:\mathrm{can}\:\mathrm{only}\:\mathrm{approximate}. \\ $$$$\mathrm{There}\:\mathrm{are}\:\mathrm{2}\:\mathrm{solutions},\:\mathrm{one}\:\in\left(\mathrm{4};\:\mathrm{5}\right) \\ $$$$\mathrm{the}\:\mathrm{other}\:\in\left(−\mathrm{1};\:\mathrm{0}\right)\:\left[\mathrm{very}\:\mathrm{close}\:\mathrm{to}\:−\mathrm{1}\right] \\ $$ Answered by…
Question Number 228287 by fantastic2 last updated on 06/Apr/26 $${Dear}\:{tinkutara} \\ $$$$\:{i}\:{can}\:{not}\:{upload}\:{image}\:{here}.{Facing}\:{this} \\ $$$${for}\:{several}\:{days}.{please}\:{fix}\:\:{this} \\ $$ Commented by Tinku Tara last updated on 06/Apr/26 $$\mathrm{When}\:\mathrm{did}\:\mathrm{you}\:\mathrm{try}\:\mathrm{upload}.…
Question Number 228290 by AgniMath last updated on 06/Apr/26 $${Q}\:\mathrm{228273} \\ $$$${please}\:{justify}\:{the}\:{answer}.\:{I}\:{have}\:{doubt} \\ $$$${in}\:{ans}.\:{I}\:{am}\:{getting}\:\mathrm{45} \\ $$ Commented by mr W last updated on 06/Apr/26 $$\mathrm{45}\:{is}\:{right}.…
Question Number 228203 by Kassista last updated on 02/Apr/26 $${let}\:{f}\left({x},{y}\right)={x}^{\mathrm{2}} +{y} \\ $$$${find},\:{from}\:{first}\:{principles},\:{the}\:{directional}\:{derivative} \\ $$$${of}\:{f}\:{along}\:{the}\:{vector}\:\left(\mathrm{2},\mathrm{9}\right) \\ $$ Answered by TonyCWX last updated on 02/Apr/26 $$\mathrm{Vector},\:{a}\:=\:\langle\mathrm{2},\:\mathrm{9}\rangle…