Question Number 96600 by Hamida last updated on 03/Jun/20 Answered by Rio Michael last updated on 03/Jun/20 $$\:{y}\:=\:\frac{\mathrm{4}}{\mathrm{7}}{x}^{\mathrm{3}} \:−\:\frac{\mathrm{2}}{\mathrm{3}}{x}^{−\mathrm{1}} \\ $$$${y}\:'\:=\:\frac{\mathrm{12}}{\mathrm{7}}{x}^{\mathrm{3}} \:+\:\frac{\mathrm{2}}{\mathrm{3}{x}^{\mathrm{2}} }\: \\ $$$${y}'\mid_{{x}=\mathrm{7}}…
Question Number 96586 by M±th+et+s last updated on 02/Jun/20 $${find}\:{the}\:{minimum}\:{value}\:{of}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{f}\left({x}\right)={x}^{{x}} \\ $$$${for}\:{x}\in\mathbb{R}^{+} \\ $$ Answered by 1549442205 last updated on 02/Jun/20 $$\mathrm{y}=\mathrm{x}^{\mathrm{x}} \Rightarrow\mathrm{lny}=\mathrm{xlnx}\Rightarrow\frac{\mathrm{y}'}{\mathrm{y}}=\mathrm{lnx}+\mathrm{1}…
Question Number 162116 by naka3546 last updated on 26/Dec/21 $${A}\:{function}\:\:{f}\:\:\:{is}\:\:{such}\:\:{that}\:\:{f}\::\:\mathbb{R}\:\rightarrow\:\mathbb{R}\:\:{where} \\ $$$$\:\:\:{f}\left({xy}+\mathrm{1}\right)\:=\:{f}\left({x}\right)\centerdot{f}\left({y}\right)−{f}\left({y}\right)−{x}+\mathrm{2}\:\:,\:\:\forall{x},{y}\:\in\:\mathbb{R}\:. \\ $$$${Find}\:\:{value}\:\:{of}\:\:\mathrm{10}\centerdot{f}\left(\mathrm{2017}\right)+{f}\left(\mathrm{0}\right)\:. \\ $$ Answered by Rasheed.Sindhi last updated on 27/Dec/21 $${f}\left({xy}+\mathrm{1}\right)\:=\:{f}\left({x}\right)\centerdot{f}\left({y}\right)−{f}\left({y}\right)−{x}+\mathrm{2}\:\:,\:\:\forall{x},{y}\:\in\:\mathbb{R}\:. \\…
Question Number 162118 by SANOGO last updated on 27/Dec/21 $${determiner}\:{le}\:{reste}\:{de}\:{la}\:{division}\:{euclidienne}\:{de} \\ $$$$\mathrm{10}^{\mathrm{100}} \:{par}\:\mathrm{105} \\ $$ Commented by SANOGO last updated on 27/Dec/21 $${thank}\:{you} \\ $$…
Question Number 96581 by Hamida last updated on 02/Jun/20 Answered by Rio Michael last updated on 03/Jun/20 $$\:{y}\:=\:\frac{\mathrm{7}{x}\:+\:\mathrm{8}}{\mathrm{8}{x}\:+\:\mathrm{2}}\: \\ $$$$\:\frac{{dy}}{{dx}}\:=\:\frac{\mathrm{7}\left(\mathrm{8}{x}\:+\:\mathrm{2}\right)−\mathrm{8}\left(\mathrm{7}{x}\:+\:\mathrm{8}\right)}{\left(\mathrm{8}{x}\:+\:\mathrm{2}\right)^{\mathrm{2}} }\:=\:−\frac{\mathrm{50}}{\left(\mathrm{8}{x}\:+\:\mathrm{2}\right)^{\mathrm{2}} } \\ $$$$\frac{{dy}}{{dx}}\mid_{\left(\mathrm{2},\mathrm{3}\right)} =\:−\frac{\mathrm{50}}{\left(\mathrm{18}\right)^{\mathrm{2}}…
Question Number 162109 by SANOGO last updated on 26/Dec/21 Answered by TheHoneyCat last updated on 01/Jan/22 $$\left.\mathrm{1}\right)\:“{x}/{y}''\:\mathrm{signifie}\:“{x}\:\mathrm{divise}\:{y}'' \\ $$$${d}=\mathrm{pgcd}\left({a},{b}\right) \\ $$$$\mathrm{Donc}\:{d}/{a}\:\mathrm{et}\:{d}/{b} \\ $$$$\mathrm{soit}\:\left\{\frac{{a}}{{d}},\:\frac{{b}}{{d}}\right\}\subset\mathbb{N} \\ $$$$\mathrm{Ainsi}\:{m}={a}×\frac{{b}}{{d}}={b}×\frac{{a}}{{d}}\:\mathrm{est}\:\mathrm{trivialement}\:\mathrm{un}\:\mathrm{multiple}\:\mathrm{des}\:\mathrm{deux}\:\mathrm{entiers}…
Question Number 96548 by Hamida last updated on 02/Jun/20 Commented by bobhans last updated on 02/Jun/20 $$\mathrm{y}'=−\mathrm{6e}^{−\mathrm{6x}} \:+\:\mathrm{8}\:\mathrm{cos}\:\mathrm{8x}\:\ldots\ldots\ldots \\ $$ Terms of Service Privacy Policy…
Question Number 96543 by Hamida last updated on 02/Jun/20 Answered by mathmax by abdo last updated on 02/Jun/20 $$\mathrm{y}^{'} \:=\mathrm{4x}^{\mathrm{3}} \mathrm{sin}\left(\mathrm{6x}\right)\:+\mathrm{6x}^{\mathrm{4}} \:\mathrm{cos}\left(\mathrm{6x}\right)\:+\mathrm{6cos}\left(\mathrm{18x}\right)−\mathrm{18}×\mathrm{6x}\:\mathrm{sin}\left(\mathrm{18x}\right) \\ $$ Terms…
Question Number 96542 by Hamida last updated on 02/Jun/20 Commented by bobhans last updated on 02/Jun/20 $$\mathrm{average}\:\mathrm{rate}\:=\:\frac{\mathrm{1}}{\mathrm{3}−\left(−\mathrm{3}\right)}\:\underset{−\mathrm{3}} {\overset{\mathrm{3}} {\int}}\left(\mathrm{x}^{\mathrm{2}} −\mathrm{2}\right)\:\mathrm{dx} \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{6}}\:\left[\frac{\mathrm{1}}{\mathrm{3}}\mathrm{x}^{\mathrm{3}} −\mathrm{2x}\right]_{−\mathrm{3}} ^{\mathrm{3}} \\…
Question Number 96538 by Hamida last updated on 02/Jun/20 Answered by john santu last updated on 02/Jun/20 $$\mathrm{y}'=\frac{\mathrm{2}.\mathrm{7}−\mathrm{2}.\mathrm{8}}{\left(\mathrm{8x}+\mathrm{7}\right)^{\mathrm{2}} }\:=\:−\frac{\mathrm{2}}{\left(\mathrm{8x}+\mathrm{7}\right)^{\mathrm{2}} } \\ $$ Commented by Hamida…