Question Number 192737 by Mastermind last updated on 25/May/23 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sequence}\:\left\{\mathrm{a}_{\mathrm{n}} \right\}\:\mathrm{is}\:\mathrm{null} \\ $$$$\mathrm{when}\:\left\{\mathrm{a}_{\mathrm{n}} \right\}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by}\:\frac{\mathrm{n}^{\mathrm{3}} +\mathrm{2n}^{\mathrm{2}} −\mathrm{1}}{\mathrm{n}^{\mathrm{4}} −\mathrm{n}^{\mathrm{2}} +\mathrm{2}} \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$ Answered…
Question Number 61667 by aliesam last updated on 06/Jun/19 $$\int\sqrt{{tan}\left({x}\right)}\:{dx}\: \\ $$ Answered by MJS last updated on 06/Jun/19 $$\int\sqrt{\mathrm{tan}\:{x}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt{\mathrm{tan}\:{x}}\:\rightarrow\:{dx}=\mathrm{2cos}^{\mathrm{2}} \:{x}\:\sqrt{\mathrm{tan}\:{x}}{dt}\right] \\ $$$$=\mathrm{2}\int\frac{{t}^{\mathrm{2}}…
Question Number 127203 by naka3546 last updated on 27/Dec/20 $$\int\:\:\frac{{dx}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{26}}}\:\:=\:\:\centerdot\centerdot\centerdot\:\:? \\ $$$${Please}\:\:{show}\:\:{your}\:\:{workings}\:\:! \\ $$ Commented by liberty last updated on 27/Dec/20 $$\:\int\:\frac{{dx}}{\:\sqrt{\left({x}+\mathrm{1}\right)^{\mathrm{2}} +\mathrm{5}^{\mathrm{2}} }}\:…
Question Number 192738 by Mastermind last updated on 25/May/23 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{supremum}\:\mathrm{and}\:\mathrm{infimum} \\ $$$$\mathrm{of}\:\mathrm{each}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{sequence} \\ $$$$ \\ $$$$\left.\mathrm{a}\left.\right)\left.\:\left\{\frac{\mathrm{n}−\mathrm{1}}{\mathrm{2n}}\right\}\:\:\:\:\mathrm{b}\right)\:\left\{\frac{\left(−\right)^{\mathrm{n}} \mathrm{n}}{\mathrm{2n}+\mathrm{1}}\right\}\:\:\:\:\mathrm{c}\right)\left\{\frac{\mathrm{1}+\left(−\right)^{\mathrm{n}} }{\mathrm{3}}\right\} \\ $$$$ \\ $$$$\left.\mathrm{d}\left.\right)\:\left\{\mathrm{sin}\frac{\mathrm{n}\pi}{\mathrm{2}}\right\}\:\:\:\:\mathrm{e}\right)\:\left\{\frac{\mathrm{1}}{\mathrm{n}}\:−\:\mathrm{sin}\frac{\mathrm{n}\pi}{\mathrm{2}}\right\} \\ $$$$ \\…
Question Number 192733 by Mingma last updated on 25/May/23 Answered by MM42 last updated on 25/May/23 $$\frac{\mathrm{1}−\frac{\mathrm{2}{tanA}}{\mathrm{1}+{tan}^{\mathrm{2}} {A}}}{\mathrm{1}+\frac{\mathrm{1}−{tan}^{\mathrm{2}} {A}}{\mathrm{1}+{tan}^{\mathrm{2}} {A}}}={tanA}−\mathrm{1} \\ $$$$\frac{{tan}^{\mathrm{2}} {A}−\mathrm{2}{tanA}+\mathrm{1}}{\mathrm{2}}={tanA}−\mathrm{1} \\ $$$${tan}^{\mathrm{2}}…
Question Number 127198 by bramlexs22 last updated on 27/Dec/20 $$\:\:{Should}\:{auld}\:{acquaintance}\:{be}\:{forgot} \\ $$$${and}\:{never}\:{brought}\:{to}\:{mine}? \\ $$$${Should}\:{auld}\:{aquaintance}\:{be}\:{forgot} \\ $$$${and}\:{days}\:{of}\:{auld}\:{lang}\:{syne}? \\ $$$$ \\ $$$${For}\:{auld}\:{lang}\:{syne},\:{my}\:{dear} \\ $$$${for}\:{auld}\:{lang}\:{syne}\: \\ $$$${we}'{ll}\:{take}\:{a}\:{cup}\:{o}'\:{kindness}\:{yet} \\…
Question Number 192732 by mokys last updated on 25/May/23 $${let}\:{the}\:{closed}\:{interval}\:\left[{a},{b}\right]\:{be}\:{the}\:{domain}\:{of}\:{the}\:{function}\:{f}\: \\ $$$${find}\:{the}\:{domain}\:{of}\:{f}\left({x}−\mathrm{3}\right)\:{and}\:{f}\left({x}+\mathrm{3}\right)\:?\:\: \\ $$ Answered by MM42 last updated on 25/May/23 $${a}\leqslant{x}−\mathrm{3}\leqslant{b}\Rightarrow{a}+\mathrm{3}\leqslant{x}\leqslant{b}+\mathrm{3}\Rightarrow{D}_{{f}−\mathrm{3}} =\left[{a}+\mathrm{3},{b}+\mathrm{3}\right] \\ $$$${a}\leqslant{x}+\mathrm{3}\leqslant{b}\Rightarrow{a}−\mathrm{3}\leqslant{x}\leqslant{b}−\mathrm{3}\Rightarrow{D}_{{f}+\mathrm{3}}…
Question Number 61662 by maxmathsup by imad last updated on 06/Jun/19 $${calculate}\:\int_{−\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{cosx}}{{e}^{\frac{\mathrm{1}}{{x}}} \:+\mathrm{1}}\:{dx}\: \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 127196 by mohammad17 last updated on 27/Dec/20 Commented by mohammad17 last updated on 27/Dec/20 $${find}\:{the}\:{ordenery}\:{differention}\:{equation}? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 61661 by maxmathsup by imad last updated on 05/Jun/19 $$\left.\mathrm{1}\right)\:{calculate}\:\int\int_{{R}^{+^{\mathrm{2}} } } \:\:\:\:\:\frac{{dxdy}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{y}^{\mathrm{2}} \right)} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{ln}\left({x}\right)}{{x}^{\mathrm{2}} −\mathrm{1}}\:{dx}\:. \\ $$ Commented…