Question Number 205910 by Simurdiera last updated on 02/Apr/24 $${Resuelve}\:{la}\:{siguiente}\:{integral} \\ $$$${I}\:=\:\int\frac{{x}}{\mathrm{sinh}^{\mathrm{2}} \left({x}\right)\centerdot\mathrm{ln}\:\left(\mathrm{sinh}\:\left({x}\right)\right)\:−\:{x}\centerdot\mathrm{sinh}\:\left({x}\right)\centerdot\mathrm{cosh}\:\left({x}\right)}\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 205904 by RoseAli last updated on 02/Apr/24 Answered by mr W last updated on 02/Apr/24 $${a}+{b}+{c}=\mathrm{2} \\ $$$$\sqrt[{\mathrm{3}}]{{abc}}\leqslant\frac{{a}+{b}+{c}}{\mathrm{3}}=\frac{\mathrm{2}}{\mathrm{3}} \\ $$$${abc}=\left(\sqrt[{\mathrm{3}}]{{abc}}\right)^{\mathrm{3}} \leqslant\left(\frac{\mathrm{2}}{\mathrm{3}}\right)^{\mathrm{3}} =\frac{\mathrm{8}}{\mathrm{27}} \\…
Question Number 205884 by Abdullahrussell last updated on 01/Apr/24 Commented by Frix last updated on 01/Apr/24 $${a}^{\mathrm{3}} +{b}^{\mathrm{3}} \\ $$ Answered by Rasheed.Sindhi last updated…
Question Number 205885 by hardmath last updated on 01/Apr/24 $$\mathrm{Find}:\:\:\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\sqrt[{\boldsymbol{\mathrm{n}}}]{}\begin{pmatrix}{\mathrm{2n}}\\{\:\:\mathrm{n}}\end{pmatrix}\:=\:? \\ $$ Answered by MM42 last updated on 03/Apr/24 $$\begin{pmatrix}{\mathrm{2}{n}}\\{\:\:{n}}\end{pmatrix}=\frac{\left(\mathrm{2}{n}\right)\left(\mathrm{2}{n}−\mathrm{1}\right)\left(\mathrm{2}{n}−\mathrm{2}\right)…\left({n}+\mathrm{3}\right)\left({n}+\mathrm{2}\right)\left({n}+\mathrm{1}\right)}{{n}\left({n}−\mathrm{1}\right)\left({n}−\mathrm{2}\right)…\mathrm{3}×\mathrm{2}×\mathrm{1}} \\ $$$${a}=\sqrt[{{n}}]{}\begin{pmatrix}{\mathrm{2}{n}}\\{\:\:{n}}\end{pmatrix} \\ $$$$\Rightarrow{lna}=\frac{\mathrm{1}}{{n}}\left[{ln}\left(\mathrm{2}\right)+{ln}\left(\mathrm{2}+\frac{\mathrm{1}}{{n}−\mathrm{1}}\right)+{ln}\left(\mathrm{2}+\frac{\mathrm{2}}{{n}−\mathrm{2}}\right)+…+{ln}\left(\mathrm{2}+\frac{{n}−\mathrm{3}}{\mathrm{3}}\right)\left(\mathrm{2}+\frac{{n}−\mathrm{2}}{\mathrm{2}}\right)\left(\mathrm{2}+\frac{{n}−\mathrm{1}}{\mathrm{1}}\right)\right.…
Question Number 205880 by cortano12 last updated on 01/Apr/24 Commented by cortano12 last updated on 01/Apr/24 $$\:\underbrace{ } \\ $$ Answered by mr W last…
Question Number 205866 by RoseAli last updated on 01/Apr/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 205861 by mr W last updated on 01/Apr/24 Answered by A5T last updated on 01/Apr/24 $$\mathrm{9}×\mathrm{9}=\left(\mathrm{2}{r}−{x}\right){x}\Rightarrow\mathrm{2}{r}−{x}=\frac{\mathrm{81}}{{x}} \\ $$$$\mathrm{21}×\mathrm{21}=\left(\mathrm{2}{r}−\mathrm{16}−{x}\right)\left(\mathrm{16}+{x}\right)=\left(\frac{\mathrm{81}}{{x}}−\mathrm{16}\right)\left(\mathrm{16}+{x}\right) \\ $$$$\Rightarrow{x}=\mathrm{2}\Rightarrow{r}=\mathrm{21}.\mathrm{25} \\ $$ Commented…
Question Number 205862 by MathedUp last updated on 01/Apr/24 $$\mathrm{can}\:\mathrm{Solve}\:\mathrm{Diff}\:\mathrm{equa} \\ $$$$\left(\frac{\mathrm{d}{y}\left({t}\right)}{\mathrm{d}{t}}\right)^{\mathrm{2}} +\mathrm{4}{y}\left({t}\right)=\mathrm{8}{t}^{\mathrm{2}} −\mathrm{32}{t}+\mathrm{28} \\ $$$$\mathrm{Not}\:\mathrm{assuming}\:{y}\left({t}\right)={at}^{\mathrm{2}} +{bt}+{c} \\ $$$$\mathrm{and}\:\mathrm{Not}\:\mathrm{use}\:\mathrm{Rk}−\mathrm{4}\:\mathrm{method}?? \\ $$$$\left(\mathrm{meaning}\:\mathrm{can}\:\mathrm{we}\:\mathrm{get}\:\mathrm{closed}\:\mathrm{form}\:\mathrm{soultion}\right) \\ $$ Terms of…
Question Number 205873 by universe last updated on 01/Apr/24 $$\int_{\mathrm{0}} ^{\pi} \frac{\mathrm{1}}{\pi^{\mathrm{2}} }\:\frac{{x}}{\:\sqrt{\mathrm{1}+\mathrm{sin}^{\mathrm{3}} {x}\:}}\left[\left(\mathrm{3}\pi\mathrm{cos}{x}+\mathrm{4sin}{x}\right)\mathrm{sin}^{\mathrm{2}} {x}+\mathrm{4}\right]{dx}\:\:\: \\ $$ Answered by Berbere last updated on 02/Apr/24 $${x}\rightarrow\pi−{x};{let}\:\Omega={integral}…
Question Number 205820 by mustafazaheen last updated on 31/Mar/24 $$\begin{pmatrix}{\sqrt{\mathrm{3}}}\\{\mathrm{1}}\end{pmatrix}\:\:\mathrm{and}\:\:\begin{pmatrix}{\mathrm{1}}\\{\sqrt{\mathrm{3}}}\end{pmatrix}\:\:\:\mathrm{vector}\:\mathrm{find}\:\theta=? \\ $$ Answered by mr W last updated on 31/Mar/24 $$\mathrm{cos}\:\theta=\frac{\sqrt{\mathrm{3}}×\mathrm{1}+\mathrm{1}×\sqrt{\mathrm{3}}}{\:\mathrm{2}×\mathrm{2}}=\frac{\sqrt{\mathrm{3}}}{\mathrm{2}} \\ $$$$\Rightarrow\theta=\mathrm{30}° \\ $$…