Question Number 192289 by cortano12 last updated on 14/May/23 $$\:\:\:\:\:\:\:\:\underset{−\mathrm{e}} {\overset{\mathrm{e}} {\int}}\:\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}+\mathrm{1}}\:\mathrm{dx}\:=? \\ $$ Answered by mehdee42 last updated on 14/May/23 $${f}\left({x}\right)=\frac{{sinx}}{{secx}^{\mathrm{2}} {x}+\mathrm{1}}\Rightarrow{f}\left(−{x}\right)={f}\left({x}\right) \\…
Question Number 192261 by mnjuly1970 last updated on 13/May/23 $$ \\ $$$$\:\:\:{f}\left({x}\right)=\lfloor\:\frac{\:\mathrm{1}}{\mathrm{1}+\sqrt{{x}}}\:\rfloor\:{is}\:{derivable}\: \\ $$$$\:\:{on}\:\:\left(\:\mathrm{0}\:,\:\:{k}\:\right).\:{find}\:{the}\:{value}\:{of} \\ $$$$\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{k}_{\:{max}} =?\: \\ $$$$\:\:\: \\ $$ Terms of…
Question Number 126726 by mnjuly1970 last updated on 23/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{advanced}\:\:{calculus}… \\ $$$$\:\:{prove}\:\:{that}\::\: \\ $$$$\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}\:} {\overset{\infty} {\sum}}\frac{\mathrm{H}_{{n}} }{{n}^{\mathrm{4}} }\:\overset{?} {=}\mathrm{3}\zeta\left(\mathrm{5}\right)−\zeta\left(\mathrm{2}\right)\left(\mathrm{3}\right)\:\:…. \\ $$$$\:\:\:{where}::\:\:\:\:\mathrm{H}_{{n}\:} \:=\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}\:+…+\frac{\mathrm{1}}{{n}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:………. \\…
Question Number 61181 by mathsolverby Abdo last updated on 30/May/19 $${sove}\:\left(\mathrm{1}+{e}^{−{x}} \right){y}^{''} \:+\left(\mathrm{2}+{e}^{{x}} \right){y}^{'} \:=\left({x}+\mathrm{1}\right){e}^{{x}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 61180 by mathsolverby Abdo last updated on 30/May/19 $${solve}\:{y}^{''} \:+\mathrm{3}{y}^{'} −{y}\:={sin}\left(\mathrm{2}{x}\right) \\ $$ Answered by tanmay last updated on 30/May/19 $$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }+\mathrm{3}\frac{{dy}}{{dx}}−{y}={sin}\mathrm{2}{x}…
Question Number 61178 by mathsolverby Abdo last updated on 30/May/19 $${solve}\:\left(\mathrm{1}+{x}^{\mathrm{2}} \right){y}^{'} \:+\left(\mathrm{1}−{x}^{\mathrm{2}} \right){y}\:={x}\:{e}^{−\mathrm{3}{x}} \\ $$ Commented by maxmathsup by imad last updated on 31/May/19…
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Question Number 126641 by TITA last updated on 22/Dec/20 Commented by TITA last updated on 22/Dec/20 $$\mathrm{please}\:\mathrm{help} \\ $$ Answered by Lordose last updated on…
Question Number 126635 by BHOOPENDRA last updated on 22/Dec/20 Answered by Ar Brandon last updated on 22/Dec/20 $$\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} =\mathrm{r}^{\mathrm{2}} \mathrm{cos}^{\mathrm{2}} \theta\mathrm{cos}^{\mathrm{2}} \phi+\mathrm{r}^{\mathrm{2}} \mathrm{cos}^{\mathrm{2}}…
Question Number 126631 by mnjuly1970 last updated on 23/Dec/20 $$\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{calculus}… \\ $$$$\:\:\:\:\:{prove}\:{that}:: \\ $$$$\:\:\:\:::\:\:\:\:\:\:\Omega\overset{??} {=}\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {x}^{{n}−\mathrm{1}} {ln}^{\mathrm{2}} \left(\mathrm{1}−{x}\right){dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\frac{\mathrm{2}}{{n}}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\left(\frac{{H}_{{k}}…