Question Number 159465 by mnjuly1970 last updated on 17/Nov/21 $$ \\ $$$$\:\:\:\:\:{simplify} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\xi\::=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\:\frac{\:\mathrm{1}}{\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{k}^{\mathrm{3}} }\:\right)=? \\ $$$$ \\ $$…
Question Number 159447 by mnjuly1970 last updated on 17/Nov/21 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:#{calculate}# \\ $$$$\:\:\:\:\:\Omega\::=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\:{x}^{\:\frac{{t}}{\mathrm{2}}} −{x}^{\:{t}} }{\mathrm{1}\:−\:{x}}\:{dx}\:{dt}\:=\:? \\ $$$$\:\:\:\:\:\:\:\:\:−−−{m}.{n}−−− \\ $$ Commented…
Question Number 28341 by Cheyboy last updated on 24/Jan/18 $${Find}\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{5}{x}−\mathrm{tan}\:\left(\mathrm{5}{x}\right)}{{x}^{\mathrm{3}} } \\ $$ Commented by Cheyboy last updated on 24/Jan/18 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{\mathrm{5}−\mathrm{sec}^{\mathrm{2}} \left(\mathrm{5}{x}\right).\mathrm{5}}{\mathrm{3}{x}^{\mathrm{2}} }…
Question Number 93844 by mhmd last updated on 15/May/20 $${let}\:{f}\left({x}\right)=\sqrt{{x}}\:\:{and}\:{g}\left({x}\right)=\sqrt{{x}}\:{find}\:{the}\:{domain}\:{of}\:\left({f}.{g}\right)\left({x}\right)\:? \\ $$$${help}\:{me}\:{sir} \\ $$ Answered by M±th+et+s last updated on 15/May/20 $$\left({f}.{g}\right)\left({x}\right)={f}\left(\sqrt{{x}}\right)=\sqrt{\sqrt{{x}}}\:{so}\:{domain}\:{and}\:{range}\:{are}\:\left[\mathrm{0},\infty\right) \\ $$$$ \\…
Question Number 28305 by NECx last updated on 23/Jan/18 $${if}\:{y}=\mathrm{sin}^{−\mathrm{1}} {x}^{\mathrm{2}} +\mathrm{cos}^{−\mathrm{1}} {x}^{\mathrm{2}} \\ $$$${find}\:{dy}/{dx} \\ $$ Commented by abdo imad last updated on 23/Jan/18…
Question Number 28304 by NECx last updated on 23/Jan/18 $${if}\:{y}=\left(\mathrm{sin}^{−\mathrm{1}} {x}\right)^{\mathrm{2}} +\left(\mathrm{cos}^{−\mathrm{1}} {x}\right)^{\mathrm{2}} \\ $$$$ \\ $$$${find}\:{dy}/{dx} \\ $$ Answered by ajfour last updated on…
Question Number 93837 by mhmd last updated on 15/May/20 Commented by i jagooll last updated on 15/May/20 $$\mathrm{t}=\mathrm{2}\:\Rightarrow\mathrm{x}=\mathrm{6} \\ $$$$\left.\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{3x}^{\mathrm{2}} −\mathrm{4x}\:\right]_{\mathrm{x}=\:\mathrm{6}} \\ $$$$=\:\mathrm{3}\left(\mathrm{36}\right)−\mathrm{24}\:=\:\mathrm{108}−\mathrm{24} \\ $$$$=\mathrm{84}…
Question Number 28198 by NECx last updated on 21/Jan/18 $${Find}\:{the}\:{shortest}\:{distance}\:{from} \\ $$$${the}\:{origin}\:{to}\:{the}\:{curve}\:{xy}=\mathrm{3} \\ $$ Answered by mrW2 last updated on 22/Jan/18 $${distance}\:{of}\:{point}\:\left({x},{y}\right)\:{to}\:{the}\:{origin}\:{is}\:{r}. \\ $$$${r}^{\mathrm{2}} ={x}^{\mathrm{2}}…
Question Number 28199 by NECx last updated on 21/Jan/18 $${suppose}\:{one}\:{of}\:{the}\:{side}\:{of}\:{any} \\ $$$${box}\:{that}\:{can}\:{be}\:{carried}\:{onto}\:{an} \\ $$$${airplane}\:{must}\:{be}\:{less}\:{than}\:\mathrm{8}{m}. \\ $$$${Find}\:{the}\:{maximum}\:{value}\:{of}\:{such} \\ $$$${a}\:{box}\:{if}\:{the}\:{sum}\:{of}\:{the}\:{three}\:{sides} \\ $$$${can}\:{not}\:{exceed}\:\mathrm{46}{m}. \\ $$ Answered by mrW2…
Question Number 93732 by Ar Brandon last updated on 14/May/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{n}-\mathrm{th}\:\mathrm{derivative}\:\mathrm{of} \\ $$$$\mathrm{f}\left({x}\right)=\mathrm{sin}\left({x}\right){l}\mathrm{n}{x} \\ $$ Commented by mathmax by abdo last updated on 14/May/20 $${f}^{\left({n}\right)}…