Question Number 164059 by bobhans last updated on 13/Jan/22 $$\:\:\mathrm{Air}\:\mathrm{leaks}\:\mathrm{from}\:\mathrm{a}\:\mathrm{spherical}\:\mathrm{ballon}\:\mathrm{so}\:\mathrm{that}\: \\ $$$$\:\mathrm{it}\:\mathrm{maintains}\:\mathrm{its}\:\mathrm{shape}\:\mathrm{at}\:\mathrm{a}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{25}\:\mathrm{cc}/\mathrm{m} \\ $$$$\:.\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{change}\:\mathrm{in}\:\mathrm{the}\:\mathrm{length} \\ $$$$\:\:\mathrm{of}\:\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{the}\:\mathrm{balloon}\:\mathrm{when}\:\mathrm{the}\:\mathrm{radius} \\ $$$$\:\:\mathrm{is}\:\mathrm{5}\:\mathrm{cm} \\ $$ Terms of Service Privacy Policy…
Question Number 32980 by Nayon.Sm last updated on 08/Apr/18 $$ \\ $$$$ \\ $$$$\frac{\mathrm{d}}{\mathrm{dx}}\left(\begin{vmatrix}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{2}\right)^{\mathrm{x}^{\mathrm{3}} +\mathrm{3}} }&{\mathrm{2}^{\mathrm{x}} }&{\mathrm{cosx}^{\mathrm{x}} }\\{\mathrm{log}_{\mathrm{2}^{\mathrm{x}+\mathrm{1}} } \left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}^{\mathrm{2x}} +\overset{} {\mathrm{3}}\right)}&{\mathrm{xlnx}}&{\mathrm{sin}^{−\mathrm{1}} \mathrm{tanx}}\\{\mathrm{3}}&{\pi^{\mathrm{sinhx}}…
Question Number 32971 by math1967 last updated on 08/Apr/18 $${If}\:{siny}={xsin}\left({a}+{y}\right)\:{show}\:{that} \\ $$$$\frac{{dy}}{{dx}}=\frac{{sina}}{\mathrm{1}−\mathrm{2}{xcosa}+{x}^{\mathrm{2}} } \\ $$$$ \\ $$ Answered by math1967 last updated on 06/May/18 $${siny}={xsinacosy}\:+{xcosasiny}…
Question Number 98450 by bemath last updated on 14/Jun/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{supremum}\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{infimum}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{x}}{\mathrm{sin}\:\mathrm{x}}\:,\mathrm{x}\in\:\left(\mathrm{0},\frac{\pi}{\mathrm{2}}\:\right] \\ $$ Commented by bobhans last updated on 14/Jun/20 $$\mathrm{f}\:'\left(\mathrm{x}\right)=\frac{\mathrm{sin}\:\mathrm{x}−\mathrm{xcos}\:\mathrm{x}}{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}}\:\:\_\_\_\left(\mathrm{1}\right) \\ $$$$\mathrm{take}\:\mathrm{g}\left(\mathrm{x}\right)\:=\:\mathrm{sin}\:\mathrm{x}−\mathrm{xcos}\:\mathrm{x}\:;\:\mathrm{x}\in\:\left[\mathrm{0},\frac{\pi}{\mathrm{2}}\:\right]\:…
Question Number 98398 by bemath last updated on 13/Jun/20 $$\mathrm{f}\left(\mathrm{x}\right)\:=\:\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+…}}}}} \\ $$$$\mathrm{f}\:'\left(\mathrm{5}\right)\:=\: \\ $$ Commented by bobhans last updated on 14/Jun/20 $$\mathrm{let}\:\mathrm{y}\:=\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{…}}}}} \\ $$$$\mathrm{defined}\:\mathrm{for}\:\begin{cases}{\mathrm{x}\geqslant\mathrm{0}}\\{\mathrm{y}\geqslant\mathrm{0}}\end{cases} \\…
Question Number 163928 by mathlove last updated on 12/Jan/22 $${f}\left({x}\right)=\frac{\mathrm{2}{x}^{\mathrm{100}!} }{\mathrm{100}!}+{x}^{\mathrm{100}} +\mathrm{1} \\ $$$${find}\:\:\:\frac{{d}^{\mathrm{100}!} {f}\left({x}\right)}{{dx}^{\mathrm{100}!} }=? \\ $$ Answered by mr W last updated on…
Question Number 32776 by NECx last updated on 02/Apr/18 $${Find}\:{the}\:{optimum}\:{points}\:{of} \\ $$$${the}\:{function}\:{y}={f}\left({x}\right) \\ $$$$\:\:{f}\left({x}\right)=\mathrm{2}{x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} −\mathrm{36}{x}+\mathrm{34} \\ $$ Answered by MJS last updated on 02/Apr/18…
Question Number 32775 by NECx last updated on 02/Apr/18 $${Find}\:{the}\:{area}\:{bounded}\:{by}\:{the} \\ $$$${curve}\:{y}=\mathrm{3}{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{3},{the}\:{x}\:{axis} \\ $$$${and}\:{the}\:{line}\:{x}=\mathrm{5}\:{and}\:{x}=\mathrm{2} \\ $$ Answered by MJS last updated on 02/Apr/18 $$\mathrm{1}.\:\mathrm{check}\:\mathrm{the}\:\mathrm{zeros}…
Question Number 32756 by NECx last updated on 01/Apr/18 $${Please}\:{help} \\ $$$$ \\ $$$${Find}\:{the}\:{area}\:{bounded}\:{by} \\ $$$${y}\left({x}+\mathrm{2}\right)={x}^{\mathrm{4}} ,{x}=\mathrm{0},{y}=\mathrm{0},{and}\:{x}=\mathrm{3} \\ $$ Answered by MJS last updated on…
Question Number 98244 by ~blr237~ last updated on 12/Jun/20 $$\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:{xe}^{{cosx}} {cos}\left({sinx}\right){dx}=\:\mathrm{2}\pi^{\mathrm{2}} \\ $$ Answered by maths mind last updated on 15/Jun/20 $${e}^{{cos}\left({x}\right)+{isin}\left({x}\right)} ={e}^{{cos}\left({x}\right)}…