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When-f-x-is-a-differentiable-function-satisfying-x-f-x-x-2-0-x-x-t-f-t-dt-Find-f-1-

Question Number 104383 by abony1303 last updated on 21/Jul/20 $$\mathrm{When}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{differentiable}\:\mathrm{function} \\ $$$$\mathrm{satisfying}\:\:{x}\centerdot{f}\left({x}\right)={x}^{\mathrm{2}} +\int_{\mathrm{0}} ^{\:{x}} \left({x}−{t}\right)\centerdot{f}\:'\left({t}\right){dt} \\ $$$$\mathrm{Find}\:\Rightarrow\:{f}\left(\mathrm{1}\right) \\ $$ Commented by abony1303 last updated on…

montrer-que-z-C-z-2-1-z-4-5z-1-1-5-

Question Number 169900 by pticantor last updated on 12/May/22 $$\boldsymbol{{montrer}}\:\boldsymbol{{que}}\:\forall\boldsymbol{{z}}\in\mathbb{C}/\:\mid\boldsymbol{{z}}\mid=\mathrm{2}, \\ $$$$\mid\frac{\mathrm{1}}{\boldsymbol{{z}}^{\mathrm{4}} −\mathrm{5}\boldsymbol{{z}}+\mathrm{1}}\mid\leqslant\frac{\mathrm{1}}{\mathrm{5}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question-169896

Question Number 169896 by Beginner last updated on 11/May/22 Answered by mr W last updated on 12/May/22 $${x}−\mathrm{3}\geqslant\mathrm{0}\:\wedge\:\mathrm{2}{x}\left({x}+\mathrm{1}\right)>\mathrm{0} \\ $$$$\Rightarrow{x}\geqslant\mathrm{3}\:\wedge\:{x}<−\mathrm{1}\:{or}\:{x}>\mathrm{0} \\ $$$$\Rightarrow{x}\geqslant\mathrm{3}\:\checkmark \\ $$$${x}−\mathrm{3}\leqslant\mathrm{0}\:\wedge\:\mathrm{2}{x}\left({x}+\mathrm{1}\right)<\mathrm{0} \\…

dy-dx-2xe-y-y-1-0-

Question Number 169892 by weltr last updated on 11/May/22 $$\frac{{dy}}{{dx}}\:=\:\mathrm{2}{xe}^{−{y}} \:,\:\:{y}\left(\mathrm{1}\right)\:=\:\mathrm{0} \\ $$ Answered by mahdipoor last updated on 11/May/22 $$\Rightarrow\frac{{dy}}{{e}^{−{y}} }={e}^{{y}} {dy}=\mathrm{2}{xdx}\Rightarrow{e}^{{y}} ={x}^{\mathrm{2}} +{c}…

Can-you-remember-this-formula-and-the-question-behind-it-mn-i-1-m-j-1-n-sign-gcd-i-j-1-The-first-prize-goes-to-that-one-who-can-tell-the-of-the-initial-question-

Question Number 38812 by MrW3 last updated on 30/Jun/18 $${Can}\:{you}\:{remember}\:{this}\:{formula}\:{and} \\ $$$${the}\:{question}\:{behind}\:{it}? \\ $$$$\:\:\:\:\boldsymbol{\Phi}=\boldsymbol{{mn}}−\underset{\boldsymbol{{i}}=\mathrm{1}} {\overset{\boldsymbol{{m}}} {\boldsymbol{\sum}}}\:\underset{\boldsymbol{{j}}=\mathrm{1}} {\overset{\boldsymbol{{n}}} {\boldsymbol{\sum}}}\:\boldsymbol{{sign}}\left[\boldsymbol{{gcd}}\left(\boldsymbol{{i}},\boldsymbol{{j}}\right)−\mathrm{1}\right] \\ $$$${The}\:{first}\:{prize}\:{goes}\:{to}\:{that}\:{one}\:{who} \\ $$$${can}\:{tell}\:{the}\:#\:{of}\:{the}\:{initial}\:{question}. \\ $$ Commented…

d-6-d-

Question Number 169874 by sciencestudent last updated on 11/May/22 $$\underset{{d}\mid\mathrm{6}} {\sum}{d}=? \\ $$ Answered by alephzero last updated on 11/May/22 $$\underset{{d}\mid\mathrm{6}} {\sum}{d}\:= \\ $$$$\left[\mathrm{1}\mid\mathrm{6}\:\wedge\:\mathrm{2}\mid\mathrm{6}\:\wedge\:\mathrm{3}\mid\mathrm{6}\:\wedge\:\mathrm{6}\mid\mathrm{6}\right] \\…