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Author: Tinku Tara

1-2-1-4-x-x-1-1-1-x-2-1-x-1-2-dx-

Question Number 129014 by bramlexs22 last updated on 12/Jan/21 $$\:\int_{−\frac{\mathrm{1}}{\mathrm{2}}} ^{\:−\frac{\mathrm{1}}{\mathrm{4}}} {x}\left({x}+\mathrm{1}\right)\:\sqrt{\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }+\frac{\mathrm{1}}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} }}\:{dx}\:=?\: \\ $$ Commented by Ajao yinka last updated on 12/Jan/21 37/192…

let-P-x-x-2-1-2-x-b-and-Q-x-x-2-cx-d-be-to-polynomials-with-real-coefficient-such-that-P-x-Q-x-Q-P-x-find-all-the-real-roots-of-P-Q-x-0-

Question Number 63474 by aliesam last updated on 04/Jul/19 $${let}\:{P}\left({x}\right)={x}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{2}}{x}+{b} \\ $$$$ \\ $$$${and}\:{Q}\left({x}\right)={x}^{\mathrm{2}} +{cx}+{d} \\ $$$$ \\ $$$${be}\:{to}\:{polynomials}\:{with}\:{real}\:{coefficient}\:{such}\:{that} \\ $$$$ \\ $$$${P}\left({x}\right)\:{Q}\left({x}\right)={Q}\left({P}\left({x}\right)\right) \\…

Given-f-x-1-1-f-x-1-f-x-f-2-2-and-2-2018-x-f-2018-dx-2-a-3-b-5-c-7-d-11-e-101-f-then-a-b-c-d-e-f-

Question Number 129009 by bramlexs22 last updated on 12/Jan/21 $$\:\mathrm{Given}\:\mathrm{f}\left(\mathrm{x}+\mathrm{1}\right)=\frac{\mathrm{1}+\mathrm{f}\left(\mathrm{x}\right)}{\mathrm{1}−\mathrm{f}\left(\mathrm{x}\right)}\:;\:\mathrm{f}\left(\mathrm{2}\right)=\mathrm{2} \\ $$$$\mathrm{and}\:\int_{\mathrm{2}} ^{\:\mathrm{2018}} \mathrm{x}.\mathrm{f}\left(\mathrm{2018}\right)\mathrm{dx}=\mathrm{2}^{\mathrm{a}} .\mathrm{3}^{\mathrm{b}} .\mathrm{5}^{\mathrm{c}} .\mathrm{7}^{\mathrm{d}} .\mathrm{11}^{\mathrm{e}} .\mathrm{101}^{\mathrm{f}} \\ $$$$\mathrm{then}\:\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}+\mathrm{e}\:+\mathrm{f}=\_\_ \\ $$ Answered by…

Given-sin-x-cos-x-5-6-Find-the-value-of-1-sin-x-1-cos-x-

Question Number 128998 by bramlexs22 last updated on 12/Jan/21 $$\:\mathrm{Given}\:\mathrm{sin}\:\mathrm{x}\:+\mathrm{cos}\:\mathrm{x}\:=\:\frac{\mathrm{5}}{\mathrm{6}}\:.\:\mathrm{Find} \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{x}}\:+\:\frac{\mathrm{1}}{\mathrm{cos}\:\mathrm{x}}\:. \\ $$ Answered by liberty last updated on 12/Jan/21 $$\mathrm{From}\:\mathrm{condition}\:\mathrm{sin}\:\mathrm{x}\:+\:\mathrm{cos}\:\mathrm{x}\:=\:\frac{\mathrm{5}}{\mathrm{6}} \\ $$$$\:\mathrm{we}\:\mathrm{get}\:\mathrm{1}+\mathrm{2sin}\:\mathrm{x}\:\mathrm{cos}\:\mathrm{x}\:=\:\frac{\mathrm{25}}{\mathrm{36}} \\…