Question Number 62347 by rajesh4661kumar@gamil.com last updated on 20/Jun/19 Answered by Kunal12588 last updated on 20/Jun/19 $$\frac{{csc}\:\theta\:−\:{sin}\:\theta}{{sec}\:\theta\:−\:{cos}\:\theta}\:=\:\frac{{a}^{\mathrm{3}} }{{b}^{\mathrm{3}} } \\ $$$$\Rightarrow{cot}\:\theta\:\frac{\mathrm{1}−{sin}^{\mathrm{2}} \theta}{\mathrm{1}−{cos}^{\mathrm{2}} \theta}=\frac{{a}^{\mathrm{3}} }{{b}^{\mathrm{3}} }…
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Question Number 62343 by maxmathsup by imad last updated on 20/Jun/19 $${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \left\{{x}\prod_{{k}=\mathrm{1}} ^{\infty} \:{cos}\left(\frac{{x}}{\mathrm{2}^{{k}} }\right)\right\}{dx} \\ $$ Commented by maxmathsup by imad last…
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Question Number 62342 by maxmathsup by imad last updated on 20/Jun/19 $${let}\:{f}\left(\xi\right)\:=\int\:\:\frac{{x}^{\mathrm{2}} }{\:\sqrt{\mathrm{1}−\xi{x}^{\mathrm{2}} }}{dx}\:\:\:{with}\:\:\mathrm{0}<\xi<\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left(\xi\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{lim}_{\xi\rightarrow\mathrm{1}} \:\:\:{f}\left(\xi\right) \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \:\frac{{x}^{\mathrm{2}} }{\:\sqrt{\mathrm{1}−{sin}^{\mathrm{2}} \theta\:{x}^{\mathrm{2}}…
Question Number 127876 by Ar Brandon last updated on 02/Jan/21 $$\mathrm{Consider}\:\mathrm{the}\:\mathrm{sequence}\:\mathrm{defined}\:\mathrm{by}:\:\mathrm{0}<\mathrm{u}_{\mathrm{0}} <\mathrm{1}\:\mathrm{and}\:\forall\mathrm{n}\in\mathbb{N},\:\mathrm{u}_{\mathrm{n}+\mathrm{1}} =\mathrm{u}_{\mathrm{n}} −\mathrm{u}_{\mathrm{n}} ^{\mathrm{2}} . \\ $$$$\mathrm{1}.\:\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sequence}\:\left(\mathrm{u}_{\mathrm{n}} \right)\:\mathrm{converges}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{its}\:\mathrm{limit}\:? \\ $$$$\mathrm{2}.\:\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{series}\:\mathrm{with}\:\mathrm{general}\:\mathrm{term}\:\mathrm{u}_{\mathrm{n}} ^{\mathrm{2}} \:\mathrm{converges}. \\ $$$$\mathrm{3}.\:\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{series}\:\mathrm{with}\:\mathrm{general}\:\mathrm{terms}\:\mathrm{ln}\left(\frac{\mathrm{u}_{\mathrm{n}+\mathrm{1}}…
Question Number 62341 by Tawa1 last updated on 20/Jun/19 $$\mathrm{How}\:\mathrm{many}\:\mathrm{real}\:\mathrm{root}\:\mathrm{does}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\:\:\mathrm{x}^{\mathrm{8}} \:−\:\mathrm{x}^{\mathrm{7}} \:+\:\mathrm{2x}^{\mathrm{6}} \:−\:\mathrm{2x}^{\mathrm{5}} \:+\:\mathrm{3x}^{\mathrm{4}} \:−\:\mathrm{3x}^{\mathrm{3}} \:+\:\mathrm{4x}^{\mathrm{2}} \:−\:\mathrm{4x}\:+\:\frac{\mathrm{5}}{\mathrm{2}}\:\:=\:\:\mathrm{0}\:\:\:\:\:\:\:\mathrm{has} \\ $$ Commented by Kunal12588 last…
Question Number 127877 by rs4089 last updated on 02/Jan/21 Commented by rs4089 last updated on 02/Jan/21 $${prove}\:{it}… \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 62340 by Tawa1 last updated on 19/Jun/19 Commented by maxmathsup by imad last updated on 20/Jun/19 $$\left.\mathrm{3}\right)\:{f}\left({x}\right)+{xf}\left(−{x}\right)\:={x}\:\Rightarrow{f}\left(−{x}\right)−{xf}\left({x}\right)\:=−{x}\:\:\:{we}\:{get}\:{the}\:{systeme} \\ $$$$\begin{cases}{{f}\left({x}\right)+{xf}\left(−{x}\right)\:={x}}\\{{xf}\left({x}\right)−{f}\left(−{x}\right)={x}\:\:\:\:\:\:\:\left({with}\:{unknown}\:{f}\left({x}\right)\:{and}\:{f}\left(−{x}\right)\right)}\end{cases} \\ $$$$\Delta\:=\begin{vmatrix}{\mathrm{1}\:\:\:\:\:\:\:\:{x}}\\{{x}\:\:\:\:\:\:\:\:\:−\mathrm{1}}\end{vmatrix}=−\mathrm{1}−{x}^{\mathrm{2}} \\ $$$${f}\left({x}\right)\:=\frac{\Delta_{{f}\left({x}\right)}…
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