Question Number 150697 by mathdanisur last updated on 14/Aug/21 Answered by dumitrel last updated on 14/Aug/21 $$\mathrm{1011}\leqslant{a}_{{i}} \leqslant\mathrm{2022} \\ $$$$\frac{\mathrm{1}}{\mathrm{2022}}\leqslant\frac{\mathrm{1}}{{b}_{{i}} }\leqslant\frac{\mathrm{1}}{\mathrm{1011}}\Rightarrow \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\leqslant\frac{{a}_{{i}} }{{b}_{{i}} }\leqslant\mathrm{2}\Rightarrow\left(\frac{{a}_{{i}}…
Question Number 85162 by mathmax by abdo last updated on 19/Mar/20 $$\left.\mathrm{1}\right){find}\:\int\:{ln}\left(\sqrt{{x}}+\sqrt{{x}+\mathrm{1}}\right){dx} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\sqrt{{x}}+\sqrt{{x}+\mathrm{1}}\right){dx} \\ $$ Commented by mathmax by abdo last updated…
Question Number 150696 by tabata last updated on 14/Aug/21 $$\left(\mathrm{1}\right)\int\:{x}\:{tanx}\:{dx} \\ $$$$ \\ $$$$\left(\mathrm{2}\right)\:\int\:\left(\sqrt{{tanx}}+\sqrt{{cotx}}\right){dx} \\ $$$$ \\ $$$$\left(\mathrm{3}\right)\int\:\frac{{sinx}+{cosx}}{\:\sqrt{{sinx}\:{cosx}}}\:{dx} \\ $$ Commented by Ar Brandon last…
Question Number 85163 by mathmax by abdo last updated on 19/Mar/20 $${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:{arctan}\left(\frac{\mathrm{1}}{{n}^{\mathrm{2}} \:+{n}}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 85160 by mathmax by abdo last updated on 19/Mar/20 $$\left.\mathrm{1}\right)\:{find}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{{x}^{\mathrm{4}} \:+{a}}\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{g}\left({a}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left({x}^{\mathrm{4}} \:+{a}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:{find}\:{value}\:{of}\:{integrals}\:\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{{x}^{\mathrm{4}}…
Question Number 150698 by saly last updated on 14/Aug/21 Commented by saly last updated on 14/Aug/21 $$\:\:{Do}\:{you}\:{help}\:{me}? \\ $$ Answered by Olaf_Thorendsen last updated on…
Question Number 85158 by mathmax by abdo last updated on 19/Mar/20 $${calculate}\:{U}_{{n}} =\:\int_{−\frac{\mathrm{1}}{{n}}} ^{\frac{\mathrm{1}}{{n}}} \:{x}^{\mathrm{2}} \sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}}{dx}\:\:\:\left({n}\:{integr}\:{and}\:{n}\geqslant\mathrm{2}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{nature}\:{of}\:\Sigma\:{U}_{{n}} \\ $$ Terms of Service Privacy Policy…
Question Number 19623 by Tinkutara last updated on 13/Aug/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{locus}\:\mathrm{of}\:{z}\:\mathrm{if}\:\mathrm{arg}\left(\frac{{z}\:−\:\mathrm{2}}{{z}\:−\:\mathrm{3}}\right)\:=\:\frac{\pi}{\mathrm{4}} \\ $$ Answered by ajfour last updated on 13/Aug/17 $$\mathrm{let}\:\mathrm{z}=\mathrm{x}+\mathrm{iy} \\ $$$$\Rightarrow\:\:\mathrm{arg}\left[\frac{\mathrm{x}−\mathrm{2}+\mathrm{iy}}{\mathrm{x}−\mathrm{3}+\mathrm{iy}}\right]=\frac{\pi}{\mathrm{4}} \\ $$$$\Rightarrow\:\:\mathrm{arg}\left[\frac{\left(\mathrm{x}−\mathrm{2}+\mathrm{iy}\right)\left(\mathrm{x}−\mathrm{3}−\mathrm{iy}\right)}{\left(\mathrm{x}−\mathrm{3}\right)^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}}…
Question Number 150688 by ajfour last updated on 14/Aug/21 Commented by ajfour last updated on 14/Aug/21 $${Find}\:{maximum}\:{tetrahedron} \\ $$$${volume}. \\ $$ Answered by mr W…
Question Number 85153 by reprins last updated on 19/Mar/20 $$\int\sqrt{\mathrm{4}\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{4}}\boldsymbol{\mathrm{dx}}\:=\:… \\ $$$$ \\ $$$$ \\ $$ Commented by mathmax by abdo last updated on…