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Let-f-0-1-R-be-a-differentiable-function-such-that-f-f-x-x-for-all-x-0-1-and-f-0-1-If-n-is-a-positive-integer-evaluate-the-following-integral-0-1-x-f-x-2n

Question Number 145318 by ZiYangLee last updated on 04/Jul/21 $$\mathrm{Let}\:{f}:\left[\mathrm{0},\mathrm{1}\right]\rightarrow\mathbb{R}\:\mathrm{be}\:\mathrm{a}\:\mathrm{differentiable}\:\mathrm{function} \\ $$$$\mathrm{such}\:\mathrm{that}\:{f}\left({f}\left({x}\right)\right)={x}\:\mathrm{for}\:\mathrm{all}\:{x}\in\left[\mathrm{0},\mathrm{1}\right]\:\mathrm{and} \\ $$$${f}\left(\mathrm{0}\right)=\mathrm{1}. \\ $$$$\mathrm{If}\:{n}\:\mathrm{is}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{integer},\:\mathrm{evaluate}\:\mathrm{the} \\ $$$$\mathrm{following}\:\mathrm{integral}:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \left({x}−{f}\left({x}\right)\right)^{\mathrm{2}{n}} \:{dx} \\ $$…

x-x-x-1-2-2-find-x-

Question Number 145256 by Gbenga last updated on 03/Jul/21 $${x}^{{x}^{{x}} } =\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\sqrt{\mathrm{2}}} \\ $$$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{x}} \\ $$ Commented by justtry last updated on 04/Jul/21 $${i}\:{think}\:{there}\:{is}\:{not}\:{x}\in\:\mathbb{R}\:{to}\:{find}\:{it}. \\…

Riddle-clue-1-I-have-different-types-2-I-may-be-considered-natural-whole-positive-or-negative-3-I-am-the-basic-building-block-of-mathematics-4-I-am-often-conside

Question Number 145229 by otchereabdullai@gmail.com last updated on 03/Jul/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Riddle} \\ $$$$\:\:\:\:\left(\mathrm{clue}\right) \\ $$$$\mathrm{1}.\:\mathrm{I}\:\mathrm{have}\:\mathrm{different}\:\mathrm{types} \\ $$$$\mathrm{2}.\:\mathrm{I}\:\mathrm{may}\:\mathrm{be}\:\mathrm{considered}\:\mathrm{natural},\:\mathrm{whole}, \\ $$$$\mathrm{positive}\:\mathrm{or}\:\mathrm{negative} \\ $$$$\mathrm{3}.\:\mathrm{I}\:\mathrm{am}\:\mathrm{the}\:\mathrm{basic}\:\mathrm{building}\:\mathrm{block}\:\mathrm{of} \\ $$$$\mathrm{mathematics} \\ $$$$\mathrm{4}.\:\mathrm{I}\:\mathrm{am}\:\mathrm{often}\:\mathrm{considered}\:\mathrm{reasonable}\:\mathrm{or} \\…

please-what-does-mean-

Question Number 14156 by chux last updated on 28/May/17 $$\mathrm{please}\:\mathrm{what}\:\mathrm{does}\:\omega\:\mathrm{mean}? \\ $$ Answered by RasheedSindhi last updated on 29/May/17 $$\omega\:\mathrm{is}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{complex}\:\mathrm{cube} \\ $$$$\mathrm{roots}\:\mathrm{of}\:\mathrm{unity}\left(\mathrm{1}\right). \\ $$$$\mathrm{Let}\:\mathrm{x}\:\mathrm{is}\:\mathrm{a}\:\mathrm{cube}\:\mathrm{root}\:\mathrm{of}\:\mathrm{1} \\…

find-the-equation-of-the-tangent-and-normal-to-the-curve-xy-9-at-x-4-

Question Number 79667 by gopikrishnan last updated on 27/Jan/20 $${find}\:{the}\:{equation}\:{of}\:{the}\:{tangent}\:{and} \\ $$$${normal}\:{to}\:{the}\:{curve}\:{xy}=\mathrm{9}\:{at}\:{x}=\mathrm{4} \\ $$ Commented by john santu last updated on 27/Jan/20 $$\mathrm{slope}\:\mathrm{the}\:\mathrm{tangent}\:\mathrm{line} \\ $$$$\Rightarrow\mathrm{y}+\mathrm{xy}'\:=\:\mathrm{0}\:\Rightarrow\mathrm{y}'\:=−\frac{\mathrm{y}}{\mathrm{x}}=−\frac{\left(\frac{\mathrm{9}}{\mathrm{4}}\right)}{\mathrm{4}}…