Question Number 160908 by naka3546 last updated on 10/Dec/21 $${x},{y},{z}\:\:\in\:\:\mathbb{R}^{+} \\ $$$${Find}\:\:{the}\:\:{minimum}\:\:{value}\:\:{of}\:\:{this}\:\:{expression}\: \\ $$$$\:\:\:\:\:\:\frac{{xyz}}{\left(\mathrm{1}+\mathrm{3}{x}\right)\left({x}+\mathrm{8}{y}\right)\left({y}+\mathrm{9}{z}\right)\left(\mathrm{6}+{z}\right)}\:\: \\ $$$$ \\ $$ Commented by mr W last updated on…
Question Number 95339 by mathocean1 last updated on 24/May/20 $$\mathrm{f}\left(\mathrm{x}\right)=\mid\mathrm{2x}+\mathrm{3}\mid \\ $$$$\mathrm{f}\:'\left(\mathrm{x}\right)=…? \\ $$ Answered by john santu last updated on 24/May/20 $$\mathrm{f}\left(\mathrm{x}\right)\:=\:\sqrt{\left(\mathrm{2x}+\mathrm{3}\right)^{\mathrm{2}} } \\…
Question Number 160873 by SANOGO last updated on 08/Dec/21 Answered by TheSupreme last updated on 08/Dec/21 $$\left.\mathrm{1}\right)\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{1}}{{a}^{\mathrm{2}} }\frac{{dx}}{\mathrm{1}+\left(\frac{{x}}{{a}}\right)^{\mathrm{2}} }=\frac{\mathrm{1}}{{a}}{arctan}\frac{{x}}{{a}}=\frac{\pi}{\mathrm{2}{a}} \\ $$ Commented by…
Question Number 160865 by vvvv last updated on 08/Dec/21 $$\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{3}} {\boldsymbol{\mathrm{lim}}}\frac{\boldsymbol{{tan}}\left(\boldsymbol{{x}}\right)−\boldsymbol{{tan}}\left(\mathrm{3}\right)}{\boldsymbol{{sin}}\left(\boldsymbol{{ln}}\left(\boldsymbol{{x}}−\mathrm{2}\right)\right)} \\ $$$$\boldsymbol{{work}}\:\boldsymbol{{with}}\:{the}\:{rule}\:{of} \\ $$$${substitution}\:\:{of}\:{infinitely} \\ $$$${small}\:\:{functions}\:{equivalent}\: \\ $$$${to}\:{a}\:{limit} \\ $$ Commented by cortano last…
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Question Number 160848 by naka3546 last updated on 07/Dec/21 $${Find}\:\:{the}\:\:{value}\:\:{of}\:\:{a}\:\:{such}\:\:{that} \\ $$$$\:\:\:\:\:−\mathrm{2}\:<\:\frac{\mathrm{2}{x}+{a}}{{x}^{\mathrm{2}} +\mathrm{1}}\:<\:\mathrm{2} \\ $$ Answered by kowalsky78 last updated on 08/Dec/21 $${I}\:{think}\:{the}\:{correct}\:{answer}\:{is}\:{a}=−\frac{\mathrm{3}}{\mathrm{2}}. \\ $$…
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Question Number 160831 by MathsFan last updated on 07/Dec/21 $$\mathrm{simplify}\:\:\sqrt[{\mathrm{3}}]{\mathrm{2}+\sqrt{\mathrm{5}}} \\ $$ Commented by mr W last updated on 07/Dec/21 $$\sqrt[{\mathrm{3}}]{\mathrm{2}+\sqrt{\mathrm{5}}} \\ $$$$=\frac{\sqrt[{\mathrm{3}}]{\mathrm{16}+\mathrm{8}\sqrt{\mathrm{5}}}}{\mathrm{2}} \\ $$$$=\frac{\sqrt[{\mathrm{3}}]{\mathrm{5}\sqrt{\mathrm{5}}+\mathrm{3}\sqrt{\mathrm{5}}+\mathrm{3}×\mathrm{5}+\mathrm{1}}}{\mathrm{2}}…
Question Number 160816 by 0731619 last updated on 07/Dec/21 Commented by mr W last updated on 07/Dec/21 $${f}\left({t}\right)={t}^{{t}^{{t}^{…} } } =\frac{{W}\left(−\mathrm{ln}\:{t}\right)}{−\mathrm{ln}\:{t}}\:{is}\:{defined}\:{only} \\ $$$${for}\:{t}>\mathrm{0}. \\ $$$${with}\:{t}=\mathrm{ln}\:{x},\:{so}\:\left({ln}\:{x}\right)^{\left({ln}\:{x}\right)^{…}…
Question Number 29726 by naka3546 last updated on 11/Feb/18 Commented by ajfour last updated on 11/Feb/18 Commented by ajfour last updated on 12/Feb/18 $${AD}\mathrm{sin}\:\mathrm{18}°\:=\:{a}\mathrm{sin}\:\left({x}°−\mathrm{36}°\right) \\…