Question Number 106315 by pticantor last updated on 04/Aug/20 $$\boldsymbol{{show}}\:\boldsymbol{{that}} \\ $$$$\circledast\forall\:\left(\boldsymbol{{x}}_{\mathrm{1}} ,\boldsymbol{{x}}_{\mathrm{2}} ,…..,\boldsymbol{{x}}_{\boldsymbol{{n}}\:} \right)\in\mathbb{R}^{\boldsymbol{{n}}} \\ $$$$\left(\underset{\boldsymbol{{k}}=\mathrm{1}} {\overset{\boldsymbol{{n}}} {\sum}}\boldsymbol{{x}}_{\boldsymbol{{k}}} \right)^{\mathrm{2}} \leqslant\boldsymbol{{n}}\underset{\boldsymbol{{k}}=\mathrm{1}} {\overset{\boldsymbol{{n}}} {\sum}}\boldsymbol{{x}}_{\boldsymbol{{k}}} ^{\mathrm{2}} \\…
Question Number 106309 by bemath last updated on 04/Aug/20 $$\mathrm{If}\:\mathrm{g}\left(\mathrm{x}\right)=\:\mathrm{x}+\sqrt{\mathrm{x}}\:\mathrm{and}\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{\mathrm{f}\left(\mathrm{x}\right)−\mathrm{f}\left(\mathrm{2}\right)}{\mathrm{x}^{\mathrm{2}} +\mathrm{ax}+\mathrm{b}}=\frac{\mathrm{4}}{\mathrm{3}} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\left(\mathrm{f}\circ\mathrm{g}\right)'\left(\mathrm{1}\right). \\ $$ Answered by bobhans last updated on 05/Aug/20 $$\mathrm{g}\left(\mathrm{x}\right)=\:\mathrm{x}+\sqrt{\mathrm{x}}\:\Rightarrow\mathrm{g}'\left(\mathrm{x}\right)=\:\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{x}}}\:;\:\mathrm{g}'\left(\mathrm{1}\right)=\:\frac{\mathrm{3}}{\mathrm{2}} \\…
Question Number 106138 by bobhans last updated on 03/Aug/20 $$\mathrm{If}\:\mathrm{root}\:\mathrm{of}\:\mathrm{equation}\:\mathrm{x}^{\mathrm{3}} −\mathrm{px}^{\mathrm{2}} +\mathrm{qx}−\mathrm{r}=\mathrm{0}\:\mathrm{are}\:\mathrm{in} \\ $$$$\mathrm{AP}\:\mathrm{than}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{relation}\:\mathrm{between}\:\mathrm{p},\mathrm{q} \\ $$$$\mathrm{and}\:\mathrm{r}\:? \\ $$ Answered by bemath last updated on 03/Aug/20…
Question Number 106133 by mathmax by abdo last updated on 02/Aug/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{e}^{−\mathrm{2x}} \mathrm{ln}\left(\mathrm{3}−\mathrm{x}^{\mathrm{2}} \right) \\ $$$$\left.\mathrm{1}\right)\:\mathrm{calculate}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{x}\right)\mathrm{and}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integr}\:\mathrm{serie} \\ $$ Answered by mathmax…
Question Number 106134 by mathmax by abdo last updated on 03/Aug/20 $$\mathrm{let}\:\mathrm{g}\left(\mathrm{x}\right)\:=\mathrm{arcatan}\left(\mathrm{1}+\mathrm{x}\right)\mathrm{ln}\left(\mathrm{1}−\mathrm{2x}\right) \\ $$$$\left.\mathrm{1}\right)\:\mathrm{find}\:\mathrm{g}^{\left(\mathrm{n}\right)} \left(\mathrm{x}\right)\:\mathrm{and}\:\mathrm{g}^{\left(\mathrm{n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integr}\:\mathrm{serie} \\ $$$$\mathrm{3}/\:\mathrm{calculate}\:\:\int_{−\frac{\mathrm{1}}{\mathrm{4}}} ^{\frac{\mathrm{1}}{\mathrm{4}}} \:\mathrm{g}\left(\mathrm{x}\right)\mathrm{dx} \\ $$ Terms…
Question Number 171546 by Kodjo last updated on 17/Jun/22 $${f}\left({x}\right)=\frac{−{ln}\mid{x}\mid}{{x}}+{x}−\mathrm{2}\:\:,\:\:\:{g}\left({x}\right)=−{x}^{\mathrm{2}} +\mathrm{1}−{ln}\mid{x}\mid \\ $$$$ \\ $$Calculate the derivative of f(x) as a function of g(x) Commented…
Question Number 171484 by infinityaction last updated on 16/Jun/22 $$ \\ $$$$\:\:\:\:{let}\:{f}\left({x}\right)\:=\:{x}+\frac{\mathrm{2}}{\mathrm{1}.\mathrm{3}}{x}^{\mathrm{3}} +\frac{\mathrm{2}.\mathrm{4}}{\mathrm{1}.\mathrm{3}.\mathrm{5}}{x}^{\mathrm{5}} +\frac{\mathrm{2}.\mathrm{4}.\mathrm{6}}{\mathrm{1}.\mathrm{3}.\mathrm{5}.\mathrm{7}}{x}^{\mathrm{7}} +……… \\ $$$$\:\:\:\:\forall{x}\in\left(\mathrm{0},\mathrm{1}\right)\:\:{the}\:{value}\:{of}\:\:{f}\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\right)\:=\:? \\ $$ Commented by mr W last updated…
Question Number 40407 by prof Abdo imad last updated on 21/Jul/18 $${let}\:{f}\left({x}\right)=\:{x}^{\mathrm{3}} −{x}−\mathrm{1} \\ $$$$\left.\mathrm{1}\left.\right)\:{prove}\:{that}\:\exists\:\alpha\:\in\:\right]\mathrm{1},\mathrm{2}\left[\:/{f}\left(\alpha\right)=\mathrm{0}\right. \\ $$$$\left.\mathrm{2}\right)\:{use}\:{the}\:{newton}\:{method}\:\:{with}\:{x}_{\mathrm{0}} =\frac{\mathrm{3}}{\mathrm{2}} \\ $$$${to}\:{find}\:{a}\:{better}\:{value}\:{for}\:\alpha\:\left({take}\:{onlly}\:\mathrm{5}\:{terms}\right) \\ $$ Answered by maxmathsup…
Question Number 40370 by math khazana by abdo last updated on 20/Jul/18 $${let}\:{u}_{{n}} \:=\sum_{{k}=\mathrm{0}} ^{{n}} \left(\mathrm{3}{k}+\mathrm{1}\right)\left(−\mathrm{1}\right)^{{k}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{interms}\:{of}\:{n} \\ $$$${S}_{{n}} ={u}_{\mathrm{0}} \:+{u}_{\mathrm{1}} +{u}_{\mathrm{2}} +….+{u}_{{n}} \\…
Question Number 171435 by cortano1 last updated on 15/Jun/22 $$\:\:{Let}\:{f}:{R}\rightarrow{R}\:{be}\:{polynomial} \\ $$$$\:{function}\:{satisfying}\: \\ $$$$\:{f}\left({x}\right)\:{f}\left(\frac{\mathrm{1}}{{x}}\right)={f}\left({x}\right)+{f}\left(\frac{\mathrm{1}}{{x}}\right)\:{and} \\ $$$$\:{f}\left(\mathrm{3}\right)=\mathrm{28},\:{then}\:{f}\left({x}\right)\:{is} \\ $$ Commented by infinityaction last updated on 15/Jun/22…