Question Number 111887 by mathdave last updated on 05/Sep/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 111890 by mathdave last updated on 05/Sep/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 111879 by mathdave last updated on 05/Sep/20 $${prove}\:{that}\: \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}{n}\underset{{k}=\mathrm{1}} {\overset{{n}−\mathrm{1}} {\sum}}\frac{\mathrm{ln}\left({k}+{n}\right)−\mathrm{ln}\left({n}\right)}{{k}^{\mathrm{2}} +{n}^{\mathrm{2}} }=\frac{\pi}{\mathrm{8}}\mathrm{ln2} \\ $$ Answered by Dwaipayan Shikari last updated…
Question Number 46344 by MrW3 last updated on 24/Oct/18 Commented by MrW3 last updated on 25/Oct/18 $${A}\:{rod}\:{of}\:{mass}\:{M}\:{and}\:{length}\:{l}\:{is}\:{supported} \\ $$$${at}\:{one}\:{end}\:{through}\:{a}\:{hinge}.\:{the}\:{other}\:{free} \\ $$$${end}\:{is}\:{hold}\:{horizontally}\:{by}\:{a}\:{rope} \\ $$$${as}\:{shown}.\:{the}\:{rope}\:{has}\:{a}\:{mass}\:\rho\:{per} \\ $$$${unit}\:{length}.…
Question Number 111869 by mathdave last updated on 05/Sep/20 $${evaluate} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}\left(\mathrm{1}+{x}\right)}{{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{6}}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 111868 by mathdave last updated on 05/Sep/20 $${simplify} \\ $$$$\int\frac{\mathrm{1}−\mathrm{5sin}^{\mathrm{2}} {x}}{\mathrm{cos}^{\mathrm{5}} {x}\mathrm{sin}^{\mathrm{2}} {x}}{dx} \\ $$ Answered by Her_Majesty last updated on 05/Sep/20 $$\int\frac{\left(\mathrm{1}−\mathrm{5}{sin}^{\mathrm{2}}…
Question Number 177403 by gopikrishnan last updated on 04/Oct/22 $${if}\:{david}\:{wears}\:{shorts}\:{and}\:{short}\:{sleeves}\:{to}\:{play}\:{outside}\:{what}\:{temperature}\:{would}\:{it}\:{most}\:{likely}\:{be}? \\ $$ Commented by Frix last updated on 04/Oct/22 $$\mathrm{if}\:\mathrm{David}\in\mathrm{Africa}\:\Rightarrow\:{T}\approx\mathrm{35}°\mathrm{C} \\ $$$$\mathrm{if}\:\mathrm{David}\in\mathrm{Svalbard}\:\Rightarrow\:{T}\approx\mathrm{0}°{C} \\ $$ Answered…
Question Number 177378 by SEKRET last updated on 04/Oct/22 Answered by yogamulyadi last updated on 04/Oct/22 $${x}−\frac{{x}}{\mathrm{10}}=\frac{\mathrm{1}}{\mathrm{10}}+\frac{{x}}{\mathrm{100}} \\ $$$$\mathrm{100}{x}−\mathrm{10}{x}−{x}=\mathrm{10} \\ $$$${x}=\frac{\mathrm{10}}{\mathrm{89}} \\ $$ Terms of…
Question Number 111813 by mathdave last updated on 05/Sep/20 $${if}\: \\ $$$$\psi\left({x}\right)=\frac{{x}}{\mathrm{1}−{x}}+\frac{{x}^{\mathrm{3}} }{\mathrm{1}−{x}^{\mathrm{2}} }+\frac{{x}^{\mathrm{5}} }{\mathrm{1}−{x}^{\mathrm{5}} }+\frac{{x}^{\mathrm{7}} }{\mathrm{1}−{x}^{\mathrm{7}} } \\ $$$${show}\:{that}\: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \left[\psi\left({x}\right)+\psi\left(\sqrt[{\mathrm{3}}]{{x}}\right)+\psi\left(\sqrt[{\mathrm{5}}]{{x}}\right)+\psi\left(\sqrt[{\mathrm{7}}]{{x}}\right)\right]\frac{\mathrm{ln}\left(\frac{\mathrm{1}}{{x}}\right)}{{x}}=\frac{\mathrm{25832}\pi^{\mathrm{2}} }{\mathrm{1575}}…
Question Number 46255 by hassentimol last updated on 23/Oct/18 Commented by hassentimol last updated on 23/Oct/18 $$\mathrm{Could}\:\mathrm{you}\:\mathrm{help}\:\mathrm{me}\:\mathrm{to}\:\mathrm{understand}\:\mathrm{thrice} \\ $$$$\mathrm{equations}\:\mathrm{please}\:? \\ $$$$\mathrm{Mainly}\:\mathrm{the}\:\mathrm{third}\:\mathrm{one}. \\ $$ Commented by…