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Given-F-x-1-2-x-1-x-1-f-t-dt-Show-that-F-is-defined-continuous-and-derivable-And-find-its-derivative-

Question Number 99261 by Ar Brandon last updated on 19/Jun/20 $$\mathrm{Given}\:\mathrm{F}\left(\mathrm{x}\right)=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\mathrm{x}+\mathrm{1}}{\mathrm{x}−\mathrm{1}}\mathrm{f}\left(\mathrm{t}\right)\mathrm{dt} \\ $$$$\mathrm{Show}\:\mathrm{that}\:\mathrm{F}\:\mathrm{is}\:\mathrm{defined},\:\mathrm{continuous},\:\mathrm{and}\:\mathrm{derivable}. \\ $$$$\mathrm{And}\:\mathrm{find}\:\mathrm{its}\:\mathrm{derivative} \\ $$ Answered by abdomathmax last updated on 19/Jun/20 $$\mathrm{F}\left(\mathrm{x}\right)\:=\frac{\mathrm{1}}{\mathrm{2}}\frac{\mathrm{x}+\mathrm{1}}{\mathrm{x}−\mathrm{1}}\:\int^{\mathrm{x}}…