Question Number 192409 by Abdullahrussell last updated on 17/May/23 Answered by Frix last updated on 17/May/23 $$\left({x}+{y}+{z}\right)^{\mathrm{2}} ={x}^{\mathrm{3}} +{y}^{\mathrm{3}} +{z}^{\mathrm{2}} −\mathrm{3}{xyz} \\ $$$$\left({x}+{y}+{z}\right)^{\mathrm{2}} =\left({x}+{y}+{z}\right)\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}}…
Question Number 126873 by mathmax by abdo last updated on 25/Dec/20 $$\mathrm{calculate}\:\int_{\mathrm{2019}} ^{\mathrm{2021}} \:\:\:\frac{\mathrm{dx}}{\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{2019}} \left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2021}} } \\ $$ Answered by Ar Brandon last updated on…
Question Number 61335 by necx1 last updated on 01/Jun/19 Answered by mr W last updated on 02/Jun/19 $$\mathrm{cos}\:\angle{A}=\frac{\mathrm{5}^{\mathrm{2}} +\mathrm{7}^{\mathrm{2}} −\mathrm{8}^{\mathrm{2}} }{\mathrm{2}×\mathrm{5}×\mathrm{7}}=\frac{\mathrm{1}}{\mathrm{7}} \\ $$$$\Rightarrow\mathrm{sin}\:\angle{A}=\frac{\mathrm{4}\sqrt{\mathrm{3}}}{\mathrm{7}} \\ $$$$\mathrm{cos}\:\angle{B}=\frac{\mathrm{5}^{\mathrm{2}}…
Question Number 192407 by mnjuly1970 last updated on 17/May/23 $$ \\ $$$$\:\:\:\:\:{find}\:\:{the}\:{value}\:{of}\:{the}\:{following}\:{integral} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\chi\:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:\mathrm{ln}^{\:\mathrm{2}} \left({x}\:\right)}{\mathrm{1}+\:{x}^{\:\mathrm{2}} }\:{dx}\:=\:?\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:−−−−−−−−− \\ $$ Answered…
Question Number 192406 by josemate19 last updated on 17/May/23 $$\int\:\frac{\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}}{{x}}\:{dx}??? \\ $$ Answered by mehdee42 last updated on 17/May/23 $${x}=\mathrm{2}{chu}\Rightarrow{dx}=\mathrm{2}{shudu} \\ $$$$\Rightarrow{I}=\mathrm{2}\int\:\frac{{sh}^{\mathrm{2}} {u}}{{chu}}\:{du}\:=\mathrm{2}\int\:\left({chu}−\frac{\mathrm{1}}{{chu}}\:\right){du} \\…
Question Number 126869 by Mustafa2020 last updated on 25/Dec/20 $$\int_{\mathrm{0}} ^{\infty} \frac{{x}}{\mathrm{1}+{x}^{\mathrm{2}} {sin}^{\mathrm{2}} {x}}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 61329 by maxmathsup by imad last updated on 01/Jun/19 $${let}\:{f}\left({x}\right)\:=\frac{{e}^{−{x}} }{\mathrm{1}+{x}}\:{sin}\left(\mathrm{3}{x}\right) \\ $$$$\left.\mathrm{1}\right)\:{dtermine}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}\:. \\ $$ Commented by maxmathsup by…
Question Number 126865 by Lordose last updated on 24/Dec/20 $$\int_{\mathrm{0}} ^{\:\pi} \frac{\mathrm{x}}{\mathrm{2}+\mathrm{cos}\left(\mathrm{2x}\right)}\mathrm{dx}\:=\:\mathrm{0} \\ $$$$\mathrm{Prove}\:\mathrm{or}\:\mathrm{Disprove} \\ $$ Commented by Ar Brandon last updated on 25/Dec/20 Commented…
Question Number 61328 by maxmathsup by imad last updated on 01/Jun/19 $${let}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{sin}\left(\mathrm{2}{x}\right)}{\mathrm{1}+{ax}^{\mathrm{2}} }\:{dx}\:\:{with}\:\:\mid{a}\mid<\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{approximate}\:{f}\left({a}\right)\:{by}\:{a}\:{polynom} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:\:\left({perhaps}\:{not}\:{exact}\right)\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{sin}\left(\mathrm{2}{x}\right)}{\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} }\:{dx} \\ $$$$\left.\mathrm{3}\right)\:{let}\:{g}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 192397 by Mastermind last updated on 16/May/23 $$\mathrm{Let}\:\mathrm{f}:\mathrm{D}\left(\mathrm{f}\right)\subseteq\mathbb{R}^{\mathrm{n}} \rightarrow\mathbb{R}^{\mathrm{m}} \\ $$$$\mathrm{let}\:'\mathrm{a}'\:\mathrm{be}\:\mathrm{an}\:\mathrm{interior}\:\mathrm{point}\:\mathrm{of}\:\mathrm{Dom}\left(\mathrm{f}\right) \\ $$$$\mathrm{and}\:\mathrm{let}\:'\mathrm{u}'\:\mathrm{be}\:\mathrm{any}\:\mathrm{vector}\:\mathrm{in}\:\mathbb{R}^{\mathrm{n}} ,\:\mathrm{when} \\ $$$$\mathrm{is}\:\mathrm{a}\:\mathrm{vector}\:\mathrm{v}\in\mathbb{R}^{\mathrm{m}} \:\mathrm{called}\:\mathrm{the}\:\mathrm{directional} \\ $$$$\mathrm{derivative}\:\mathrm{of}\:\mathrm{f}\:\mathrm{at}\:'\mathrm{a}'\:\mathrm{along}\:\mathrm{the}\:\mathrm{line} \\ $$$$\mathrm{determine}\:\mathrm{by}\:\mathrm{u}\:? \\ $$$$…