Question Number 133231 by SOMEDAVONG last updated on 20/Feb/21 $$\mathrm{Give}\:\mathrm{S}_{\mathrm{n}} =\frac{\mathrm{n}+\mathrm{1}}{\mathrm{2}^{\mathrm{n}+\mathrm{1}} }\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{2}^{\mathrm{k}} }{\mathrm{k}}\:\:.\mathrm{Find}\:\underset{\mathrm{n}\rightarrow+\propto} {\mathrm{lim}S}_{\mathrm{n}} \:. \\ $$ Answered by Ar Brandon last updated…
Question Number 133218 by SOMEDAVONG last updated on 20/Feb/21 $$\mathrm{I}=−\int\frac{\mathrm{2}}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)\left(\sqrt{\mathrm{x}^{\mathrm{4}} −\mathrm{1}}\right)}\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 2129 by Yozzi last updated on 03/Nov/15 $${A}\:{mirror}\:{is}\:{designed}\:{so}\:{that}\:{any}\:{ray} \\ $$$${of}\:{light}\:{which}\:{hits}\:{one}\:{side}\:{of}\:{the} \\ $$$${mirror}\:{and}\:{which}\:{is}\:{parallel}\:{to}\:{a}\: \\ $$$${certain}\:{fixed}\:{line}\:{L}\:{is}\:{reflected}\:{through} \\ $$$${a}\:{fixed}\:{point}\:{O}.\:{Prove}\:{that}\:{the}\:{mirror} \\ $$$${intersects}\:{any}\:{plane}\:{containing}\:{L}\:{in} \\ $$$${a}\:{parabola}. \\ $$$${I}\:{would}\:{appreciate}\:{a}\:{formal}\:{proof}. \\…
Question Number 133191 by pticantor last updated on 19/Feb/21 $$\boldsymbol{{g}}\left(\boldsymbol{{x}},\boldsymbol{{y}}\right)=\boldsymbol{{x}}^{\mathrm{4}} +\boldsymbol{{y}}^{\mathrm{4}} −\mathrm{2}\left(\boldsymbol{{x}}−\boldsymbol{{y}}\right)^{\mathrm{2}} \\ $$$$\boldsymbol{{find}}\:\boldsymbol{{criticals}}\:\boldsymbol{{points}}\:\boldsymbol{{of}}\:\boldsymbol{{g}}\left(\boldsymbol{{x}},\boldsymbol{{y}}\right) \\ $$$$\boldsymbol{{and}}\:\boldsymbol{{hers}}\:\boldsymbol{{nature}} \\ $$ Answered by Olaf last updated on 20/Feb/21…
Question Number 133183 by bounhome last updated on 19/Feb/21 $$\int\sqrt{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{3}} }{dx}=…? \\ $$ Answered by physicstutes last updated on 19/Feb/21 $$\mathrm{let}\:{x}\:=\:\mathrm{sinh}\:\theta\:\Rightarrow\:{dx}\:=\:\mathrm{cosh}\:\theta\:{d}\theta \\ $$$$\mathrm{now},\:\int\sqrt{\left[\left(\mathrm{sinh}\:\theta\right)^{\mathrm{2}} +\mathrm{1}\right]^{\mathrm{3}}…
Question Number 133117 by SOMEDAVONG last updated on 19/Feb/21 $$\int\frac{\mathrm{1}}{\mathrm{sin}^{\mathrm{3}} \mathrm{x}}\mathrm{dx}=? \\ $$ Answered by bemath last updated on 19/Feb/21 $$=\:−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cot}\:\mathrm{x}\:\mathrm{csc}\:\mathrm{x}\:−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\:\mid\mathrm{sec}\:\mathrm{x}−\mathrm{cot}\:\mathrm{x}\mid\:+\:\mathrm{C} \\ $$ Terms of…
Question Number 133115 by aurpeyz last updated on 19/Feb/21 $${an}\:{object}\:{is}\:{placed}\:\mathrm{5}{cm}\:{away}\:{from}\:{a} \\ $$$${plane}\:{mirror}.\:{the}\:{mirror}\:{is}\:{rotated} \\ $$$${tbrough}\:{angle}\:\mathrm{20}^{\mathrm{0}} \:{about}\:{the}\:{point}\:{of} \\ $$$${incidence}.\:{calculate}\:{the}\:{shortest} \\ $$$${distance}\:{between}\:{the}\:{old}\:{and}\:{the}\:{new} \\ $$$${position}\:{of}\:{the}\:{image} \\ $$ Answered by…
Question Number 133097 by otchereabdullai@gmail.com last updated on 18/Feb/21 $$\mathrm{Assuming}\:\mathrm{that}\:\mathrm{word}\:\mathrm{population}\:\mathrm{is}\: \\ $$$$\mathrm{6}\:\mathrm{billion}\:\mathrm{and}\:\mathrm{total}\:\mathrm{world}\:\mathrm{trips}\:\mathrm{is}\: \\ $$$$\mathrm{4}.\mathrm{8}\:\mathrm{billion} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{country}\:\mathrm{potential}\: \\ $$$$\mathrm{generation}\:\mathrm{index}\:\left(\mathrm{CPG}\:\mathrm{I}\right)\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{country} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{interprete}\:\mathrm{your}\:\mathrm{results}\:\mathrm{in}\:\left(\mathrm{a}\right)\:\mathrm{above}\: \\ $$$$ \\…
Question Number 67564 by azizullah last updated on 28/Aug/19 Commented by mathmax by abdo last updated on 28/Aug/19 $${F}\left(\mathrm{0}\right)=\mathrm{0}\:=\mathrm{1}+\mathrm{1}\:+\mathrm{2}\:+{f}\:\Rightarrow{f}\:=−\mathrm{4}\:\Rightarrow \\ $$$${F}\left({x}\right)\:=−\frac{\mathrm{1}}{{x}−\mathrm{1}}+\frac{\mathrm{1}}{{x}+\mathrm{1}}\:+\frac{\mathrm{2}}{{x}^{\mathrm{2}} \:+\mathrm{1}}−\frac{\mathrm{4}}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} }\:. \\…
Question Number 133092 by Algoritm last updated on 18/Feb/21 Answered by MJS_new last updated on 19/Feb/21 $$\approx\mathrm{5}.\mathrm{40343170} \\ $$ Terms of Service Privacy Policy Contact:…