Question Number 135971 by Raxreedoroid last updated on 17/Mar/21 $$ \\ $$$$\mathrm{Let}\:{R}\left({n},{m}\right)={R}\left({n}−\mathrm{1},{m}\right)+{R}\left({n}−\mathrm{1},{m}−\mathrm{1}\right) \\ $$$$\mathrm{if}\:{R}\left(\mathrm{1},\mathrm{1}\right)=−\mathrm{6},{R}\left(\mathrm{2},\mathrm{1}\right)=\mathrm{8},{R}\left(\mathrm{3},\mathrm{1}\right)=−\mathrm{1} \\ $$$$\mathrm{and}\:\forall{t}\:{R}\left(\mathrm{4},{t}\right)=\mathrm{0} \\ $$$$ \\ $$$$ \\ $$$$\left.{a}\right)\:\mathrm{Find}\:{R}\left(\mathrm{1},\mathrm{21}\right) \\ $$$$ \\…
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Question Number 4855 by Tinku Tara last updated on 18/Mar/16 $$\mathrm{We}\:\mathrm{have}\:\mathrm{released}\:\mathrm{an}\:\mathrm{update}\:\mathrm{with}\:\mathrm{following} \\ $$$$\mathrm{enhancements}: \\ $$$$\bullet\:\mathrm{A}\:\mathrm{new}\:\mathrm{section}\:\mathrm{quizzes}\:\mathrm{is}\:\mathrm{added}.\: \\ $$$$\:\:\:\:\mathrm{You}\:\mathrm{can}\:\mathrm{also}\:\mathrm{request}\:\mathrm{a}\:\mathrm{solution}\:\mathrm{for}\:\mathrm{quiz} \\ $$$$\:\:\:\:\mathrm{question}\:\mathrm{and}\:\mathrm{we}\:\mathrm{will}\:\mathrm{provide}\:\mathrm{a}\:\mathrm{solution}. \\ $$$$\:\:\:\:\mathrm{In}\:\mathrm{case}\:\mathrm{you}\:\mathrm{want}\:\mathrm{to}\:\mathrm{start}\:\mathrm{a}\:\mathrm{discussion}\:\mathrm{you} \\ $$$$\:\:\:\:\mathrm{can}\:\mathrm{post}\:\mathrm{the}\:\mathrm{same}\:\mathrm{question}\:\mathrm{to}\:\mathrm{forum}\:\mathrm{directly} \\ $$$$\:\:\:\:\mathrm{from}\:\mathrm{quiz}.…
Question Number 70360 by Hassen_Timol last updated on 03/Oct/19 $$\underset{{n}\rightarrow+\infty} {\mathrm{l}im}\:\:\:\:\frac{\sqrt{{n}\:+\:\mathrm{1}\:}−\:{n}}{\:\sqrt{{n}\:+\:\mathrm{1}}\:+\:{n}}\:\:=\:\:? \\ $$ Answered by mind is power last updated on 03/Oct/19 $$\frac{\sqrt{{n}+\mathrm{1}}−{n}}{\:\sqrt{{n}+\mathrm{1}}+{n}}=\frac{{n}\left(\sqrt{\frac{{n}+\mathrm{1}}{{n}^{\mathrm{2}} }}−\mathrm{1}\right)}{{n}\left(\sqrt{\frac{{n}+\mathrm{1}}{{n}^{\mathrm{2}} }}+\mathrm{1}\right)}=\frac{\sqrt{\frac{\mathrm{1}}{{n}}+\frac{\mathrm{1}}{{n}^{\mathrm{2}}…
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Question Number 4809 by 314159 last updated on 15/Mar/16 $${Show}\:{that}\:\frac{{x}^{\mathrm{2}} +{a}^{\mathrm{2}} }{{x}^{\mathrm{2}} −{a}^{\mathrm{2}} }\:>\:\frac{{x}+{a}}{{x}−{a}}. \\ $$ Answered by Yozzii last updated on 15/Mar/16 $${Let}\:\phi=\frac{{x}^{\mathrm{2}} +{a}^{\mathrm{2}}…
Question Number 4793 by madscientist last updated on 11/Mar/16 $${please}\:{explain}. \\ $$$${V}\left({x}\right)=−\int{F}\left({x}\right){dx} \\ $$$$ \\ $$$$ \\ $$ Commented by FilupSmith last updated on 11/Mar/16…
Question Number 135851 by Ñï= last updated on 16/Mar/21 $$\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \left(\mathrm{cos}\:^{\mathrm{2}} {x}\right){ln}\left(\mathrm{1}+\mathrm{tan}\:^{\mathrm{4}} {x}\right){dx}=? \\ $$ Answered by mathmax by abdo last updated on 16/Mar/21…
Question Number 4773 by madscientist last updated on 08/Mar/16 $${lim}_{{x}\rightarrow\mathrm{0}\:} \:\frac{{sin}\left({x}\right)}{{x}}=\:\mathrm{1} \\ $$$${how}\:{is}\:{this}\:{so}? \\ $$$$ \\ $$ Commented by Yozzii last updated on 13/Mar/16 $${For}\:{x}\:{near}\:{zero},\:{the}\:{function}\:{sinx}…