Question Number 9461 by tawakalitu last updated on 09/Dec/16 $$\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{1}\:+\:\mathrm{y}}{\mathrm{2}\:+\:\mathrm{x}} \\ $$$$\mathrm{solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation}. \\ $$ Answered by mrW last updated on 09/Dec/16 $$\frac{\mathrm{dy}}{\mathrm{1}+\mathrm{y}}=\frac{\mathrm{dx}}{\mathrm{2}+\mathrm{x}} \\ $$$$\int\frac{\mathrm{dy}}{\mathrm{1}+\mathrm{y}}=\int\frac{\mathrm{dx}}{\mathrm{2}+\mathrm{x}} \\…
Question Number 140534 by SOMEDAVONG last updated on 09/May/21 Answered by EDWIN88 last updated on 09/May/21 $$\left(\mathrm{i}\right)\:=\:\frac{\mathrm{16x}−\mathrm{24}}{\left(\mathrm{x}−\mathrm{1}\right)\left(\mathrm{x}−\mathrm{3}\right)\left(\mathrm{x}+\mathrm{3}\right)}\:=\:\frac{\mathrm{a}}{\mathrm{x}−\mathrm{1}}+\frac{\mathrm{b}}{\mathrm{x}−\mathrm{3}}+\frac{\mathrm{c}}{\mathrm{x}+\mathrm{3}} \\ $$$$\mathrm{a}\:=\:\left[\frac{\mathrm{16x}−\mathrm{24}}{\left(\mathrm{x}−\mathrm{3}\right)\left(\mathrm{x}+\mathrm{3}\right)}\:\right]_{\mathrm{x}=\mathrm{1}} =\:\frac{−\mathrm{8}}{−\mathrm{8}}\:=\mathrm{1} \\ $$$$\mathrm{b}=\:\left[\frac{\mathrm{16x}−\mathrm{24}}{\left(\mathrm{x}−\mathrm{1}\right)\left(\mathrm{x}+\mathrm{3}\right)}\:\right]_{\mathrm{x}=\mathrm{3}} =\:\frac{\mathrm{48}−\mathrm{24}}{\mathrm{6}.\mathrm{2}}=\mathrm{2} \\ $$$$\mathrm{c}\:=\:\left[\frac{\mathrm{16x}−\mathrm{24}}{\left(\mathrm{x}−\mathrm{1}\right)\left(\mathrm{x}−\mathrm{3}\right)}\:\right]_{\mathrm{x}=−\mathrm{3}}…
Question Number 74997 by chess1 last updated on 05/Dec/19 Commented by chess1 last updated on 05/Dec/19 $$\mathrm{answer}:\:\mathrm{A} \\ $$ Answered by mind is power last…
Question Number 9460 by tawakalitu last updated on 09/Dec/16 Answered by sou1618 last updated on 09/Dec/16 $$\sqrt{\mathrm{11}−\mathrm{2}}=\sqrt{\mathrm{10}+\mathrm{1}−\mathrm{2}}=\sqrt{\mathrm{9}}=\mathrm{3} \\ $$$$\sqrt{\mathrm{1111}−\mathrm{22}}=\sqrt{\mathrm{1000}+\mathrm{100}+\mathrm{10}+\mathrm{1}−\mathrm{20}−\mathrm{2}}=\sqrt{\mathrm{1089}}=\mathrm{33} \\ $$$$…… \\ $$$${X}=\sqrt{\mathrm{1111}……\mathrm{11}_{\mathrm{2000}{digits}} −\mathrm{22}…\mathrm{2}_{\mathrm{1000}{digits}} }…
Question Number 140529 by SOMEDAVONG last updated on 09/May/21 Answered by Rasheed.Sindhi last updated on 09/May/21 $$\frac{\mathrm{1}}{{x}^{\mathrm{2}} \left({x}+\mathrm{2}\right)}−\frac{\mathrm{5}}{\left({x}−\mathrm{2}\right)\left({x}+\mathrm{2}\right)}−\frac{\mathrm{4}}{{x}−\mathrm{2}} \\ $$$$=\frac{\mathrm{1}\left({x}−\mathrm{2}\right)−\mathrm{5}\left({x}^{\mathrm{2}} \right)−\mathrm{4}\left(\:{x}^{\mathrm{2}} \left({x}+\mathrm{2}\right)\:\right)}{{x}^{\mathrm{2}} \left({x}−\mathrm{2}\right)\left({x}+\mathrm{2}\right)} \\ $$$$=\frac{{x}−\mathrm{2}−\mathrm{5}{x}^{\mathrm{2}}…
Question Number 74994 by aliesam last updated on 05/Dec/19 Commented by mind is power last updated on 05/Dec/19 Commented by mind is power last updated…
Question Number 74995 by vishalbhardwaj last updated on 05/Dec/19 $$\mathrm{find}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{Log}\:\mathrm{cos}{x}\:{dx} \\ $$ Commented by mathmax by abdo last updated on 06/Dec/19 $${let}\:{I}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}}…
Question Number 9458 by geovane10math last updated on 09/Dec/16 $$\mathrm{If}\:\mathrm{the}\:\mathrm{zeta}\:\mathrm{function}\:\mathrm{of}\:\mathrm{2}\:\mathrm{is} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\zeta}\left(\mathrm{2}\right)\:=\:\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\boldsymbol{{n}}^{\mathrm{2}} } \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\zeta}\left(\mathrm{2}\right)\:=\:\frac{\boldsymbol{\pi}^{\mathrm{2}} }{\mathrm{6}} \\ $$$$\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{infinite}\:\boldsymbol{\mathrm{rational}}\:\mathrm{numbers}, \\ $$$$\mathrm{why}\:\mathrm{converges}\:\mathrm{for}\:\frac{\boldsymbol{\pi}^{\mathrm{2}} }{\mathrm{6}},\:\mathrm{an}\:\boldsymbol{\mathrm{irrational}} \\ $$$$\mathrm{number}?…
Question Number 140531 by Willson last updated on 09/May/21 $$\mathrm{Prove}\:\mathrm{that}\:\:\underset{\mathrm{0}} {\int}^{\:\mathrm{x}} \:\frac{\mathrm{t}}{\mathrm{e}^{\mathrm{t}} −\mathrm{1}}\:\mathrm{dt}\:=\:\underset{\mathrm{n}=\mathrm{1}} {\overset{+\infty} {\sum}}\:\frac{\left(\mathrm{1}−\mathrm{e}^{−\mathrm{x}} \right)^{\mathrm{n}} }{\mathrm{n}^{\mathrm{2}} } \\ $$ Answered by mathmax by abdo…
Question Number 140530 by liberty last updated on 09/May/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{x}+\mathrm{y}\right)\mathrm{sec}\:\left(\mathrm{x}+\mathrm{y}\right)−\mathrm{ysec}\:\mathrm{y}}{\mathrm{x}}=? \\ $$ Answered by EDWIN88 last updated on 09/May/21 $$\:\mathrm{L}'\mathrm{H}\ddot {\mathrm{o}pital} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sec}\:\left(\mathrm{x}+\mathrm{y}\right)+\left(\mathrm{x}+\mathrm{y}\right)\mathrm{sec}\:\left(\mathrm{x}+\mathrm{y}\right)\mathrm{tan}\:\left(\mathrm{x}+\mathrm{y}\right)−\mathrm{0}}{\mathrm{1}}…