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Author: Tinku Tara

let-a-b-gt-0-find-all-differentiable-function-f-0-0-such-that-f-a-x-bx-f-x-x-gt-0-

Question Number 204426 by universe last updated on 17/Feb/24 $$\:\:\mathrm{let}\:\mathrm{a}\:,\:\mathrm{b}\:>\mathrm{0}\:\:\mathrm{find}\:\mathrm{all}\:\mathrm{differentiable}\:\mathrm{function} \\ $$$$\:\:\:\mathrm{f}:\left(\mathrm{0},\infty\right)\rightarrow\left(\mathrm{0},\infty\right)\:\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\:\:\:\:\mathrm{f}'\left(\frac{{a}}{\mathrm{x}}\right)\:\:=\:\:\frac{\mathrm{bx}}{\mathrm{f}\left(\mathrm{x}\right)}\:\:\:\:,\:\:\:\forall\:\mathrm{x}>\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

0-2-sin-t-ln-sint-dt-

Question Number 204437 by SANOGO last updated on 17/Feb/24 $$\int_{\mathrm{0}} ^{\frac{\Pi}{\mathrm{2}}} {sin}\left({t}\right){ln}\left({sint}\right){dt} \\ $$ Answered by TonyCWX08 last updated on 18/Feb/24 $$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}{ln}\left({sin}\left({t}\right)\right){sin}\left({t}\right){dt} \\…

Question-204397

Question Number 204397 by Abdullahrussell last updated on 16/Feb/24 Answered by MM42 last updated on 16/Feb/24 $$\left({y}−\mathrm{1}\right)\left({y}+\mathrm{1}\right)\left({y}^{\mathrm{2}} +\mathrm{1}\right)={x}\left({x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{1}\right) \\ $$$$\Rightarrow{y}={x}\Rightarrow\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}+\mathrm{1}\right)=\mathrm{0} \\ $$$$\Rightarrow{x}={y}=−\mathrm{1}\:\checkmark \\…