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Category: Differentiation

Question-54152

Question Number 54152 by ajfour last updated on 30/Jan/19 Commented by ajfour last updated on 30/Jan/19 $${Given}\:{arc}\:{of}\:{length}\:{L}.\:{Find}\:{radius} \\ $$$${R}\:{such}\:{that}\:{segment}\:{area}\:{is}\:{a} \\ $$$$\:\:\:\:\left({i}\right){maximum}\:\:\left({ii}\right){minimum}. \\ $$ Commented by…

Question-54137

Question Number 54137 by ajfour last updated on 29/Jan/19 Commented by ajfour last updated on 29/Jan/19 $${Centres}\:{of}\:{two}\:{spheres}\:{of}\:{radii}\:{R}\: \\ $$$${r}\:{are}\:\mathrm{2}{a}\:{distance}\:{apart}.\:{Find}\:{a} \\ $$$${point}\:{on}\:{the}\:{circumference}\:{of}\:{the} \\ $$$${circle}\:{with}\:{AB}\:{as}\:{diameter}\:{from} \\ $$$${which}\:{maximum}\:{surface}\:{area}\:{is}…

solve-x-1-y-2-3x-2-y-xsin-x-let-y-z-so-e-x-1-z-2-3x-2-z-xsinx-e-let-first-find-z-he-x-1-z-2-3x-2-z-0-x-1-z-3x-2-2-z-z-z-3x-2-2-x-1-l

Question Number 53965 by maxmathsup by imad last updated on 28/May/19 $${solve}\:\:\left({x}+\mathrm{1}\right){y}^{''} \:+\left(\mathrm{2}−\mathrm{3}{x}^{\mathrm{2}} \right){y}^{'} \:={xsin}\left({x}\right) \\ $$$${let}\:{y}^{'} ={z}\:\:\:{so}\:\left({e}\right)\:\Leftrightarrow\left({x}+\mathrm{1}\right){z}^{'} \:+\left(\mathrm{2}−\mathrm{3}{x}^{\mathrm{2}} \right){z}\:={xsinx}\left({e}\right)\:{let}\:{first}\:{find}\:{z} \\ $$$$\left({he}\right)\:\rightarrow\left({x}+\mathrm{1}\right){z}^{'} \:+\left(\mathrm{2}−\mathrm{3}{x}^{\mathrm{2}} \right){z}\:=\mathrm{0}\:\Rightarrow\left({x}+\mathrm{1}\right){z}^{'} \:=\left(\mathrm{3}{x}^{\mathrm{2}}…

A-man-walks-along-straight-path-at-a-speed-4-ft-s-A-spotlight-is-located-on-the-ground-20-ft-from-the-path-and-is-kept-focused-on-the-man-At-what-rate-is-spotlight-rotating-when-the-man-is-15

Question Number 185000 by cortano1 last updated on 15/Jan/23 $${A}\:{man}\:{walks}\:{along}\:{straight}\:{path}\: \\ $$$$\:{at}\:{a}\:{speed}\:\mathrm{4}\:{ft}/{s}.\:{A}\:{spotlight}\:{is} \\ $$$$\:{located}\:{on}\:{the}\:{ground}\:\mathrm{20}\:{ft}\:{from}\: \\ $$$$\:{the}\:{path}\:{and}\:{is}\:{kept}\:{focused}\:{on}\:{the}\:{man}. \\ $$$$\:{At}\:{what}\:{rate}\:{is}\:{spotlight}\:{rotating} \\ $$$$\:{when}\:{the}\:{man}\:{is}\:\mathrm{15}\:{ft}\:{from}\:{the}\: \\ $$$${point}\:{on}\:{the}\:{path}\:{closest}\:{to}\:{the}\:{light}?\: \\ $$$$\: \\…

pls-help-me-solve-this-if-y-x-2-2x-1-show-that-2x-1-d-2-y-dx-2-4-dy-dx-0-

Question Number 53890 by shaddie last updated on 27/Jan/19 $$\mathrm{pls}.\:\mathrm{help}\:\mathrm{me}\:\mathrm{solve}\:\mathrm{this} \\ $$$$\mathrm{if}\:\mathrm{y}=\frac{\mathrm{x}−\mathrm{2}}{\mathrm{2x}−\mathrm{1}}\:\mathrm{show}\:\mathrm{that}\:\left(\mathrm{2x}−\mathrm{1}\right)\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }+\mathrm{4}\frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{0} \\ $$ Answered by math1967 last updated on 27/Jan/19 $$\Rightarrow{y}\left(\mathrm{2}{x}−\mathrm{1}\right)=\left({x}−\mathrm{2}\right) \\…

For-0-x-1-maximum-value-of-f-x-x-1-x-1-x-is-

Question Number 184819 by cortano1 last updated on 12/Jan/23 $$\:\:{For}\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:,\:{maximum}\:{value} \\ $$$$\:\:{of}\:{f}\left({x}\right)={x}\sqrt{\mathrm{1}−{x}+\sqrt{\mathrm{1}−{x}}}\:{is}\:\_\_ \\ $$ Answered by Frix last updated on 12/Jan/23 $${f}'\left({x}\right)=\mathrm{0} \\ $$$$−\frac{\mathrm{5}{x}−\mathrm{4}+\mathrm{2}\left(\mathrm{3}{x}−\mathrm{2}\right)\sqrt{\mathrm{1}−{x}}}{\mathrm{4}\sqrt{\mathrm{1}−{x}}\sqrt{\mathrm{1}−{x}+\sqrt{\mathrm{1}−{x}}}}=\mathrm{0} \\…