Question Number 197384 by Erico last updated on 15/Sep/23 $$\mathrm{If}\:{f}\left({x}\right)=\underset{\:\frac{\mathrm{1}}{\mathrm{x}}} {\int}^{\:\:\mathrm{x}} \frac{{lnt}}{{t}^{\mathrm{2}} −\mathrm{1}}{arctan}\left({t}\right){dt} \\ $$$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\bullet\:\forall{x}>\mathrm{0}\:\:\:\:\:\:\:\:{f}\left({x}\right)=\:\frac{\pi}{\mathrm{8}}\:\underset{\:\mathrm{0}} {\int}^{\:\pi} \mathrm{arctan}\left[\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{x}−\frac{\mathrm{1}}{\mathrm{x}}\right)\mathrm{sint}\right]\mathrm{dt} \\ $$$$\bullet\underset{\mathrm{x}\rightarrow+\infty} {\mathrm{lim}}\:{f}\left({x}\right)=\frac{\pi^{\mathrm{3}} }{\mathrm{16}} \\ $$…
Question Number 197317 by universe last updated on 13/Sep/23 $$\:\mathrm{if}\:\:\:\mathrm{x}\:\:=\:\:\frac{\mathrm{cos}\:\theta}{\mathrm{u}}\:\:,\:\mathrm{y}\:\:=\:\frac{\mathrm{sin}\:\theta}{\mathrm{u}}\:\:{and}\:\mathrm{z}\:\:=\:\:\mathrm{f}\left(\mathrm{x},\mathrm{y}\right) \\ $$$$\mathrm{then}\:\mathrm{show}\:\mathrm{that}\: \\ $$$$\:\:\:\frac{\partial^{\mathrm{2}} \mathrm{z}}{\partial\mathrm{x}^{\mathrm{2}} }\:+\:\frac{\partial^{\mathrm{2}} \mathrm{z}}{\partial\mathrm{y}^{\mathrm{2}} }\:=\:\mathrm{u}^{\mathrm{4}} \:\frac{\partial^{\mathrm{2}} \mathrm{z}}{\partial\mathrm{u}^{\mathrm{2}} }\:+\:\mathrm{u}^{\mathrm{3}} \:\frac{\partial\mathrm{z}}{\partial\mathrm{u}}\:+\:\mathrm{u}^{\mathrm{4}} \:\frac{\partial^{\mathrm{2}} \mathrm{z}}{\partial\theta^{\mathrm{2}} }…
Question Number 197277 by Sachinkhar last updated on 12/Sep/23 Answered by Sachinkhar last updated on 12/Sep/23 $$\boldsymbol{\mathrm{please}}\:\boldsymbol{\mathrm{anybody}}\:\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{this}} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 197057 by ajfour last updated on 07/Sep/23 Commented by ajfour last updated on 07/Sep/23 $${The}\:{ant}\:{has}\:{to}\:{climb}\:{up}\:{the}\:{plane} \\ $$$${and}\:{surmount}\:{the}\:{wall}\:{of}\:{height}\:{c}, \\ $$$${and}\:{descend}\:{then}\:{reach}\:{B}.\:{Find}\:{the} \\ $$$${shortest}\:{length}\:{of}\:{path}. \\ $$…
Question Number 196902 by Amidip last updated on 02/Sep/23 Answered by Gamil last updated on 05/Sep/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 196691 by justenspi last updated on 29/Aug/23 $$ \\ $$Can someone recommend Calculus book , But I prefer if the book isn't boring…
Question Number 196628 by sniper237 last updated on 28/Aug/23 $${inf}\:\varnothing\:\overset{?} {=}\:+\infty\:\:\:\:{and}\:\:\:\:\:{sup}\:\varnothing\:\overset{?} {=}\:−\infty \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 196408 by Erico last updated on 24/Aug/23 $$\mathrm{Calcul}\:\underset{\:\mathrm{0}} {\int}^{\:+\infty} \frac{\mathrm{lnt}}{\:\sqrt{\mathrm{t}}\left(\mathrm{1}+\mathrm{t}^{\mathrm{2}} \right)}\mathrm{dt} \\ $$ Answered by qaz last updated on 24/Aug/23 $$\int_{\mathrm{0}} ^{\infty} \frac{{lnt}}{\:\sqrt{{t}}\left(\mathrm{1}+{t}^{\mathrm{2}}…
Question Number 196401 by RoseAli last updated on 24/Aug/23 $$\mathrm{if}\:{y}=\mathrm{sin}\:{x}\: \\ $$$$\mathrm{find}\:\frac{\boldsymbol{{d}}^{\mathrm{2}} }{\boldsymbol{{d}}{y}^{\mathrm{2}} }\mathrm{co}\boldsymbol{{s}}^{\mathrm{7}} \boldsymbol{{x}} \\ $$ Answered by qaz last updated on 24/Aug/23 $$\mathrm{cos}\:^{\mathrm{7}}…
Question Number 196209 by mnjuly1970 last updated on 19/Aug/23 $$ \\ $$$$\:\:\:\:\:\:\Omega=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:\left({x}−\mathrm{1}\right)^{\:\mathrm{2}} }{\mathrm{ln}^{\mathrm{2}} \left({x}\right)}\:{dx}=\:? \\ $$$$\:\:\:\:\:−−−− \\ $$ Answered by Mathspace last updated…