Menu Close

Author: Tinku Tara

Consider-the-functionf-defined-by-parf-x-x-ln-x-x-in-the-interval-0-C-f-is-its-representative-curve-in-an-orthonormal-reference-system-O-i-j-Calculate-lim-x-0-f

Question Number 85985 by Rio Michael last updated on 26/Mar/20 $$\mathrm{Consider}\:\mathrm{the}\:\mathrm{function}{f}\:\mathrm{defined}\:\mathrm{by}\:\mathrm{par}{f}\left({x}\right)\:=\:−{x}\:+\:\frac{\mathrm{ln}\:{x}}{{x}}\:\mathrm{in}\:\mathrm{the}\:\mathrm{interval} \\ $$$$\left.:\:\right]\mathrm{0},+\infty\left[.\:\:\left({C}_{{f}} \right)\:\mathrm{is}\:\mathrm{its}\:\mathrm{representative}\:\mathrm{curve}\:\mathrm{in}\:\mathrm{an}\:\mathrm{orthonormal}\right. \\ $$$$\mathrm{reference}\:\mathrm{system}\:\left(\mathrm{O},\overset{\rightarrow} {{i}},\overset{\rightarrow} {{j}}\right). \\ $$$$\:\mathrm{Calculate}\:\:\underset{{x}\rightarrow\mathrm{0}^{+} \:} {\mathrm{lim}}\:{f}\left({x}\right),\:\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\:{f}\left({x}\right). \\ $$…

A-primitive-of-the-function-defned-by-f-x-x-1-1-x-1-is-A-F-x-x-2-2-x-ln-x-1-B-F-x-x-2-2-ln-x-1-C-F-x-x-2-2-x-ln-1-x-D-F-x-x-ln-x-1-

Question Number 85982 by Rio Michael last updated on 26/Mar/20 $$\mathrm{A}\:\mathrm{primitive}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}\:\mathrm{defned}\:\mathrm{by}\:\mathrm{f}\left({x}\right)\:=\:{x}\:−\mathrm{1}\:+\:\frac{\mathrm{1}}{{x}+\mathrm{1}}\:\mathrm{is}\: \\ $$$$\mathrm{A}.\:\mathrm{F}\left({x}\right)\:=\:\frac{{x}^{\mathrm{2}} }{\mathrm{2}}\:−{x}\:+\:\mathrm{ln}\left({x}\:+\:\mathrm{1}\right)\:\:\:\:\mathrm{B}.\:\mathrm{F}\left({x}\right)\:=\:\frac{{x}^{\mathrm{2}} }{\mathrm{2}}\:+\:\mathrm{ln}\left({x}−\mathrm{1}\right) \\ $$$$\mathrm{C}.\:\mathrm{F}\left({x}\right)\:=\:\frac{{x}^{\mathrm{2}} }{\mathrm{2}}−{x}\:+\:\mathrm{ln}\left(\mathrm{1}−{x}\right)\:\:\:\:\:\:\:\:\:\mathrm{D}.\:\mathrm{F}\left({x}\right)\:=\:−{x}\:+\:\mathrm{ln}\left({x}−\mathrm{1}\right) \\ $$$$ \\ $$ Commented by Serlea…

0-ln-x-2-x-x-1-x-dx-

Question Number 151519 by talminator2856791 last updated on 21/Aug/21 $$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{\mathrm{ln}\left(\lfloor{x}^{\mathrm{2}} \rfloor!\right)}{\:\left({x}^{{x}} +\mathrm{1}\right)^{{x}} }\:{dx} \\ $$$$\: \\ $$ Terms of Service Privacy…