Question Number 158823 by amin96 last updated on 09/Nov/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 158816 by HongKing last updated on 09/Nov/21 $$\mathrm{Prove}\:\mathrm{that}\:\:\mathrm{2017}^{\mathrm{2017}} \:\:\mathrm{and}\:\:\:\mathrm{2017}^{\mathrm{2018}} \\ $$$$\mathrm{can}\:\mathrm{be}\:\mathrm{written}\:\mathrm{as}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{two} \\ $$$$\mathrm{perfect}\:\mathrm{squares}. \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 158812 by amin96 last updated on 09/Nov/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 158813 by HongKing last updated on 09/Nov/21 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{value}\:\:\boldsymbol{\beta}>\mathrm{0}\:\:\mathrm{such}\:\mathrm{that}: \\ $$$$\underset{\:\mathrm{0}} {\overset{\:+\infty} {\int}}\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{2021}\boldsymbol{\beta}} \:+\:\mathrm{ln}\centerdot\left(\mathrm{1}\:+\:\beta\mathrm{x}\right)}\:\mathrm{dx}\:<\:+\infty \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 158814 by HongKing last updated on 09/Nov/21 $$\mathrm{Compare}\:\mathrm{it}: \\ $$$$\left(\mathrm{log}_{\mathrm{4}} \mathrm{20}\right)^{\mathrm{2}} \:\:\:\mathrm{and}\:\:\:\mathrm{log}_{\mathrm{4}} \mathrm{320} \\ $$$$ \\ $$ Answered by Rasheed.Sindhi last updated on…
Question Number 158781 by HongKing last updated on 08/Nov/21 Answered by MJS_new last updated on 09/Nov/21 $$\underset{\mathrm{0}} {\overset{\pi} {\int}}\frac{\left(\mathrm{1}+\mathrm{sin}^{\mathrm{2}} \:\mathrm{2}{x}\right)\mathrm{cos}\:\mathrm{4}{x}}{\mathrm{1}+{a}\mathrm{sin}^{\mathrm{2}} \:{x}}{dx}=\mathrm{2}\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\frac{\left(\mathrm{1}+\mathrm{sin}^{\mathrm{2}} \:\mathrm{2}{x}\right)\mathrm{cos}\:\mathrm{4}{x}}{\mathrm{1}+{a}\mathrm{sin}^{\mathrm{2}} \:{x}}…
Question Number 158775 by HongKing last updated on 08/Nov/21 $$\mathrm{Find}: \\ $$$$\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\:\frac{\mathrm{1}}{\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{x}\:+\:\mathrm{1}\right)\centerdot\left(\mathrm{1}\:+\:\mathrm{ax}\right)}\:\mathrm{dx}\:\:;\:\:\mathrm{a}>\mathrm{0} \\ $$$$ \\ $$$$\mathrm{Answer}: \\ $$$$\frac{-\pi\sqrt{\mathrm{3}}\centerdot\left(\mathrm{a}-\mathrm{2}\right)+\mathrm{9a}\centerdot\mathrm{ln}\left(\mathrm{a}\right)}{\mathrm{9}\centerdot\left(\mathrm{a}^{\mathrm{2}} -\mathrm{a}+\mathrm{1}\right)} \\ $$ Answered…
Question Number 158774 by HongKing last updated on 08/Nov/21 Answered by MJS_new last updated on 08/Nov/21 $$\mathrm{sin}^{\mathrm{4}} \:{x}\:+\mathrm{cos}^{\mathrm{2}} \:{x}\:=\mathrm{sin}^{\mathrm{2}} \:{x}\:+\mathrm{cos}^{\mathrm{4}} \:{x} \\ $$$$\Rightarrow\:\mathrm{we}\:\mathrm{have} \\ $$$$\mathrm{2}\sqrt{\mathrm{7}+\mathrm{cos}\:\mathrm{4}{x}}+\sqrt{\mathrm{9}−\mathrm{cos}\:\mathrm{4}{x}}=\mathrm{6}\sqrt{\mathrm{2}}…
Question Number 158761 by HongKing last updated on 08/Nov/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 158759 by HongKing last updated on 08/Nov/21 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\sqrt[{\boldsymbol{\mathrm{n}}}]{\underset{\boldsymbol{\mathrm{k}}=\mathrm{0}} {\overset{\mathrm{2}\boldsymbol{\mathrm{n}}} {\sum}}\left(-\mathrm{1}\right)^{\boldsymbol{\mathrm{k}}} \:\centerdot\:\frac{\mathrm{4n}\:+\:\mathrm{1}}{\mathrm{4n}\:-\:\mathrm{2k}\:+\:\mathrm{1}}\begin{pmatrix}{\mathrm{2n}}\\{\:\mathrm{k}}\end{pmatrix}}\:=\:\mathrm{1} \\ $$$$ \\ $$ Answered by mindispower last updated…