Question Number 137005 by greg_ed last updated on 28/Mar/21 $$\boldsymbol{\mathrm{Hi}},\:\boldsymbol{\mathrm{guyz}}\:! \\ $$$$\boldsymbol{\mathrm{For}}\:\boldsymbol{\mathrm{R}}\:=\:\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{3}}{\mathrm{4}}×\frac{\mathrm{5}}{\mathrm{6}}×…×\frac{\mathrm{223}}{\mathrm{224}}\:\:\:\boldsymbol{\mathrm{and}}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{S}}\:=\:\frac{\mathrm{2}}{\mathrm{3}}×\frac{\mathrm{4}}{\mathrm{5}}×\frac{\mathrm{6}}{\mathrm{7}}×…×\frac{\mathrm{224}}{\mathrm{225}}\:. \\ $$$$\boldsymbol{\mathrm{Prove}}\:\boldsymbol{\mathrm{that}}\::\:\:\boldsymbol{\mathrm{R}}\:<\:\frac{\mathrm{1}}{\mathrm{15}}\:<\:\boldsymbol{\mathrm{S}}. \\ $$ Commented by greg_ed last updated on 01/May/21…
Question Number 137004 by Mathspace last updated on 28/Mar/21 $${find}\:\int\:\frac{\sqrt{{x}}}{\:\sqrt{{x}−\mathrm{1}}+\sqrt{{x}+\mathrm{1}}}{dx} \\ $$ Answered by aleks041103 last updated on 28/Mar/21 $$\frac{\sqrt{{x}}}{\:\sqrt{{x}−\mathrm{1}}+\sqrt{{x}+\mathrm{1}}}= \\ $$$$=\frac{\sqrt{{x}}}{\:\sqrt{{x}−\mathrm{1}}+\sqrt{{x}+\mathrm{1}}}\:\frac{\sqrt{{x}+\mathrm{1}}−\sqrt{{x}−\mathrm{1}}}{\:\sqrt{{x}+\mathrm{1}}−\sqrt{{x}−\mathrm{1}}}= \\ $$$$=\sqrt{{x}}\left(\sqrt{{x}+\mathrm{1}}−\sqrt{{x}−\mathrm{1}}\right) \\…
Question Number 137007 by SLVR last updated on 28/Mar/21 Commented by SLVR last updated on 28/Mar/21 $${kindly}\:{send}\:{me}\:{the}\:{solution} \\ $$ Commented by mr W last updated…
Question Number 137001 by Mathspace last updated on 28/Mar/21 $${calculate}\:\:\int_{\mathrm{3}} ^{\infty} \:\frac{{dx}}{\left({x}^{\mathrm{2}} −\mathrm{4}\right)^{\mathrm{5}} \left({x}+\mathrm{1}\right)^{\mathrm{3}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 137003 by Mathspace last updated on 28/Mar/21 $${find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{cos}^{\mathrm{5}} {t}}{{cos}\left(\mathrm{5}{t}\right)}{dt} \\ $$ Answered by bobhans last updated on 29/Mar/21 $$\mathrm{cos}\:\left(\mathrm{5t}\right)=\mathrm{cos}\:^{\mathrm{5}} \mathrm{t}−\mathrm{10sin}\:^{\mathrm{2}} \mathrm{t}\:\mathrm{cos}\:^{\mathrm{3}}…
Question Number 136996 by EDWIN88 last updated on 28/Mar/21 $$\mathrm{Given}\:\mathrm{a},\mathrm{b}\:\mathrm{and}\:\mathrm{c}\:\mathrm{is}\:\mathrm{real}\:\mathrm{number}\:\mathrm{satisfy} \\ $$$$\mathrm{a}+\mathrm{b}+\mathrm{c}\:=\:\mathrm{4}\:\mathrm{and}\:\mathrm{ab}+\mathrm{ac}+\mathrm{bc}\:=\:\mathrm{3}\:.\:\mathrm{The}\:\mathrm{value} \\ $$$$\mathrm{of}\:\lceil\:\mathrm{3c}+\mathrm{2}\:\rceil\:=\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 5926 by FilupSmith last updated on 05/Jun/16 $$\mathrm{I}'\mathrm{m}\:\mathrm{curious}\:\mathrm{about}\:\mathrm{your}\:\mathrm{response}\:\mathrm{to}\:\mathrm{this} \\ $$$$ \\ $$$$\mathrm{Where}\:\mathrm{is}\:\mathrm{the}\:\mathrm{mistake}: \\ $$$$\frac{\mathrm{0}}{\mathrm{0}}=\frac{\mathrm{100}−\mathrm{100}}{\mathrm{100}−\mathrm{100}} \\ $$$$\frac{\mathrm{0}}{\mathrm{0}}=\frac{\mathrm{10}^{\mathrm{2}} −\mathrm{10}^{\mathrm{2}} }{\mathrm{10}\left(\mathrm{10}−\mathrm{10}\right)} \\ $$$$\frac{\mathrm{0}}{\mathrm{0}}=\frac{\left(\mathrm{10}−\mathrm{10}\right)\left(\mathrm{10}+\mathrm{10}\right)}{\mathrm{10}\left(\mathrm{10}−\mathrm{10}\right)} \\ $$$$\frac{\mathrm{0}}{\mathrm{0}}=\frac{\left(\mathrm{10}+\mathrm{10}\right)}{\mathrm{10}} \\…
Question Number 136999 by mnjuly1970 last updated on 28/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:……{advanced}\:\:……\:\:\:{calculus}…. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} {ln}\left({x}\right).{sin}\left({x}\right).{e}^{−{x}} {dx}=? \\ $$$$\:\:\:\:\:\:\:\:\:\:\: \\ $$ Answered by mnjuly1970 last…
Question Number 5924 by sanusihammed last updated on 05/Jun/16 $${Solve}\:{for}\:{x}\:{and}\:{y} \\ $$$$ \\ $$$$\mathrm{2}^{{x}} \:+\:\mathrm{3}^{{y}} \:=\:\mathrm{31}\:\:\:…………….\:{equation}\:\left({i}\right) \\ $$$$\mathrm{3}^{{x}\:} +\:\mathrm{2}^{{y}} \:=\:\mathrm{17}\:\:…………….\:{equation}\:\left({ii}\right) \\ $$$$ \\ $$$${please}\:{help}. \\…
Question Number 136992 by liberty last updated on 28/Mar/21 $$\ell\:=\:\int\:\frac{\mathrm{cos}\:\mathrm{7x}−\mathrm{cos}\:\mathrm{8x}}{\mathrm{1}+\mathrm{2cos}\:\mathrm{5x}}\:\mathrm{dx}\:=? \\ $$ Answered by EDWIN88 last updated on 28/Mar/21 $$\:\ell\:=\:\int\:\frac{\mathrm{cos}\:\mathrm{7x}−\mathrm{cos}\:\mathrm{8x}}{\mathrm{1}+\mathrm{2cos}\:\mathrm{5x}}\:\mathrm{dx} \\ $$$$\mathrm{Simplify}\:\mathrm{the}\:\mathrm{integrand}\:\mathrm{by}\:\mathrm{Euler}'\mathrm{s}\:\mathrm{formula} \\ $$$$\frac{\mathrm{cos}\:\mathrm{7x}−\mathrm{cos}\:\mathrm{8x}}{\mathrm{1}+\mathrm{2cos}\:\mathrm{5x}}\:=\:\frac{\mathrm{e}^{\mathrm{i7x}} +\mathrm{e}^{−\mathrm{i7x}}…