Question Number 75041 by ~blr237~ last updated on 06/Dec/19 $$\left.\mathrm{1}\left.\right)\left.\:\mathrm{Show}\:\mathrm{that}\:\:\mathrm{for}\:\mathrm{a}\in\right]\mathrm{01}\right]\mathrm{the}\:\mathrm{function}\:\:\mathrm{f}_{\mathrm{a}} \::\mathbb{R}_{+} \rightarrow\mathbb{R}\:\mathrm{defined}\:\mathrm{by}\:\mathrm{f}_{\mathrm{a}} \left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{a}} \: \\ $$$$\mathrm{is}\:\:\:\mathrm{a}−\mathrm{holder}\:\mathrm{function}\:\:\mathrm{in}\:\mathrm{other}\:\mathrm{way}\:\:\mathrm{there}\:\mathrm{exist}\:\:\mathrm{K}>\mathrm{0}\:\mathrm{such}\:\mathrm{as}\:\forall\:\mathrm{x},\mathrm{y}>\mathrm{0}\: \\ $$$$\mid\mathrm{f}_{\mathrm{a}} \left(\mathrm{x}\right)−\mathrm{f}_{\mathrm{a}} \left(\mathrm{y}\right)\mid\leqslant\mathrm{K}\mid\mathrm{x}−\mathrm{y}\mid^{\mathrm{a}} \:\: \\ $$$$ \\ $$…
Question Number 140574 by john_santu last updated on 09/May/21 $$\:\underset{{x}\rightarrow\frac{\pi}{\mathrm{4}}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{tan}\:^{\mathrm{3}} {x}}{\mathrm{cos}\:\mathrm{2}{x}}\:=? \\ $$ Answered by bramlexs22 last updated on 09/May/21 $$\:\underset{{x}\rightarrow\frac{\pi}{\mathrm{4}}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}+\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}\right)\left(\mathrm{1}−\mathrm{tan}\:^{\mathrm{3}} \mathrm{x}\right)}{\mathrm{1}−\mathrm{tan}\:^{\mathrm{2}}…
Question Number 75034 by chess1 last updated on 06/Dec/19 Answered by Kunal12588 last updated on 06/Dec/19 $${y}={x}^{{x}^{{x}^{{x}} } } \\ $$$${log}\:{y}\:={x}^{{x}^{{x}} } {log}\:{x} \\ $$$${log}\:\left({log}\:{y}\right)\:=\:{x}^{{x}}…
Question Number 9498 by FilupSmith last updated on 11/Dec/16 $$\mathrm{For}\:{y}={x}^{\mathrm{2}} ,\:\mathrm{show}\:\mathrm{how}\:\mathrm{to}\:\mathrm{find}\:\frac{{dy}}{{d}\theta} \\ $$ Commented by FilupSmith last updated on 11/Dec/16 $$\mathrm{Note}:\:\theta\:\mathrm{is}\:\mathrm{the}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{the}\:\mathrm{tangent}\:\mathrm{line} \\ $$ Answered by…
Question Number 140571 by liberty last updated on 09/May/21 $$\int\:\left(\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}+\mathrm{cos}\:^{\mathrm{4}} \mathrm{x}\:\right)\mathrm{dx}\:=? \\ $$ Answered by bramlexs22 last updated on 09/May/21 Answered by physicstutes last…
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Question Number 75033 by naka3546 last updated on 06/Dec/19 $$\frac{\mathrm{4}}{\mathrm{11}}\:<\:\frac{{x}}{{y}}\:<\:\frac{\mathrm{3}}{\mathrm{8}} \\ $$$${x},\:{y}\:\:\in\:\:\mathbb{Z}^{+} \\ $$$${min}\:\left\{{x}+{y}\right\}\:\:=\:\:? \\ $$ Answered by mr W last updated on 06/Dec/19 $$\frac{\mathrm{4}}{\mathrm{11}}<\frac{{x}}{{y}}<\frac{\mathrm{3}}{\mathrm{8}}…
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Question Number 9491 by Raja Naik last updated on 10/Dec/16 $$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\frac{\mathrm{d}}{\mathrm{dx}}\left(\frac{\mathrm{acos}^{\mathrm{3}} \mathrm{x}}{\mathrm{3sinx}^{\mathrm{2}} \:}\right) \\ $$$$\mathrm{and}\:\mathrm{it}\:\mathrm{is}\:\mathrm{possible}\:\mathrm{or}\:\mathrm{not} \\ $$ Answered by mrW last updated on 11/Dec/16 $$\mathrm{y}=\frac{\mathrm{acos}^{\mathrm{3}}…
Question Number 75027 by chess1 last updated on 06/Dec/19 Commented by mathmax by abdo last updated on 06/Dec/19 $${x}+{z}=\mathrm{3}\:\Rightarrow\mathrm{0}\leqslant{x}\leqslant\mathrm{3}\:{and}\:\mathrm{0}\leqslant{z}\leqslant\mathrm{3}\:\:\:{we}\:{have}\:\:\mathrm{0}\leqslant{y}\leqslant\mathrm{2}\:\Rightarrow \\ $$$$\int\int\int\:\:\frac{{dxdydz}}{\left({x}+{y}+{z}\right)^{\mathrm{3}} }\:=\int_{\mathrm{0}} ^{\mathrm{3}} \left(\:\int_{{o}} ^{\mathrm{2}}…