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Question Number 116480 by Dwaipayan Shikari last updated on 04/Oct/20 $$\frac{\mathrm{1}}{\mathrm{8}}+\frac{\mathrm{1}}{\mathrm{18}}+\frac{\mathrm{1}}{\mathrm{30}}+\frac{\mathrm{1}}{\mathrm{44}}+\frac{\mathrm{1}}{\mathrm{60}}+\frac{\mathrm{1}}{\mathrm{78}}+\frac{\mathrm{1}}{\mathrm{98}}+\frac{\mathrm{1}}{\mathrm{120}}+…….. \\ $$ Answered by Olaf last updated on 04/Oct/20 $${u}_{{n}} \:=\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} +\mathrm{7}{n}}\:=\:\frac{\mathrm{1}}{{n}\left({n}+\mathrm{7}\right)}\:=\:\frac{\mathrm{1}}{\mathrm{7}}\left(\frac{\mathrm{1}}{{n}}−\frac{\mathrm{1}}{{n}+\mathrm{7}}\right) \\ $$$$\underset{{n}=\mathrm{1}}…
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Question Number 50892 by peter frank last updated on 21/Dec/18 $${solve}\:{the}\:{equation} \\ $$$$\mathrm{tan}\:\mathrm{3}\theta{cot}\theta+\mathrm{1}=\mathrm{0}\:{for} \\ $$$$\mathrm{0}\leqslant\theta\leqslant\mathrm{180} \\ $$$$\left.{b}\right){show}\:{that}\:{if}\:\mathrm{cos}\:\mathrm{2}\theta\:{is}\:{not}\:{zero} \\ $$$${then} \\ $$$$\mathrm{cos}\:\mathrm{2}\theta+\mathrm{sec}\:\mathrm{2}\theta=\mathrm{2}\left[\frac{\mathrm{cos}\:^{\mathrm{4}} \theta+\mathrm{sin}\:^{\mathrm{4}} \theta}{\mathrm{cos}\:^{\mathrm{4}} \theta−\mathrm{sin}\:^{\mathrm{4}} \theta}\right]…
Question Number 50835 by Tawa1 last updated on 21/Dec/18 Commented by Tawa1 last updated on 21/Dec/18 $$\mathrm{Please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{solve}\:\mathrm{it}\:\mathrm{with}\:\mathrm{diagram} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on…
Question Number 116348 by Dwaipayan Shikari last updated on 03/Oct/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\frac{\left(\mathrm{5}+\mathrm{x}\right)\left(\mathrm{2}+\mathrm{x}\right)^{\mathrm{2}} }{\mathrm{x}\left(\mathrm{1}+\mathrm{x}\right)}\:\:\left(\mathrm{x}\neq−\mathrm{1},\mathrm{0}\right) \\ $$ Commented by MJS_new last updated on 03/Oct/20 $$−\infty<\frac{\left(\mathrm{5}+{x}\right)\left(\mathrm{2}+{x}\right)^{\mathrm{2}} }{{x}\left(\mathrm{1}+{x}\right)}<\infty \\ $$$$\Rightarrow\:\mathrm{minimum}\:\mathrm{is}\:−\infty…
Question Number 50796 by lihao12345 last updated on 20/Dec/18 $$\int\mathrm{1}/\left(\mathrm{1}+{x}^{\mathrm{4}} \right){dx}= \\ $$ Commented by Abdo msup. last updated on 20/Dec/18 $${this}\:{integral}\:{is}\:{solved}\:\:{i}\:{give}\:{the}\:{key} \\ $$$${we}\:{decompose}\:{F}\left({x}\right)=\frac{\mathrm{1}}{{x}^{\mathrm{4}} \:+\mathrm{1}}…
Question Number 50764 by Tawa1 last updated on 19/Dec/18 Commented by mr W last updated on 20/Dec/18 $${f}\left({x}\right)=\frac{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{6}} −{x}^{\mathrm{12}} −\mathrm{2}{x}^{\mathrm{6}} }{{x}^{\mathrm{7}} +{x}^{\mathrm{5}} +{x}^{\mathrm{9}} +{x}^{\mathrm{3}}…
Question Number 50702 by pooja24 last updated on 19/Dec/18 $${write}\:{the}\:{fourier}\:{series}\:{of}\: \\ $$$${f}\left({x}\right)={x}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{0}\leqslant{x}\leqslant\mathrm{2} \\ $$ Commented by maxmathsup by imad last updated on 19/Dec/18 $${i}\:{think}\:\:\mathrm{0}\leqslant{x}\leqslant\mathrm{2}\pi\:\:\:{if}\:{f}\:{is}\:\mathrm{2}\pi\:{periodic}\:{odd}\:{we}\:{have} \\…