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Author: Tinku Tara

Question-150697

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}}…

1-find-f-a-0-dx-x-4-a-with-a-gt-0-2-find-g-a-0-dx-x-4-a-2-3-find-value-of-integrals-0-dx-x-4-1-0-dx-2x-4-8-0-dx-x-4-1-2-an

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}}…

calculate-U-n-1-n-1-n-x-2-1-x-1-x-dx-n-integr-and-n-2-2-find-nature-of-U-n-

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…

Find-the-locus-of-z-if-arg-z-2-z-3-pi-4-

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}}…