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…
Question Number 105843 by bobhans last updated on 01/Aug/20 $$\left(\mathrm{3}{x}\right)^{\mathrm{1}+\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{3}{x}\right)} \:>\:\mathrm{81}{x}^{\mathrm{2}} \\ $$$${find}\:{the}\:{solution}\:{set}\: \\ $$ Answered by bemath last updated on 01/Aug/20 $$\left(\mathrm{3}{x}\right)^{\mathrm{1}+\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{3}{x}\right)}…
Question Number 40260 by maxmathsup by imad last updated on 17/Jul/18 $${let}\:{f}\left({x}\right)={sin}\left(\mathrm{2}{x}\right) \\ $$$$\left.\mathrm{1}\right)\:{find}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}\:. \\ $$ Commented by maxmathsup by imad…
Question Number 105735 by bobhans last updated on 31/Jul/20 $${What}\:{is}\:{the}\:{cubic}\:{polynomial}\:{for}\:{y}\left(\mathrm{0}\right)=\mathrm{1}; \\ $$$${y}\left(\mathrm{1}\right)=\mathrm{0}\:;\:{y}\left(\mathrm{2}\right)=\mathrm{1}\:{and}\:{y}\left(\mathrm{3}\right)=\mathrm{10}\: \\ $$ Commented by PRITHWISH SEN 2 last updated on 31/Jul/20 $$\mathrm{y}\left(\mathrm{x}\right)=\:\left(\mathrm{x}−\mathrm{1}\right)\left(\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}−\mathrm{1}\right)…
Question Number 40125 by maxmathsup by imad last updated on 16/Jul/18 $${let}\:{z}_{\mathrm{0}} =\mathrm{0}\:\:{and}\:\:\forall{n}\:\in{N}\:\:\:{z}_{{n}+\mathrm{1}} =\frac{{i}}{\mathrm{2}}{z}_{{n}} \:+\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:\:{find}\:\:{z}_{{n}} {at}\:{form}\:{of}\:{sum} \\ $$$$\left.\mathrm{2}\right){let}\:{W}_{{n}} \:\:={z}_{{n}} \:\:\:\:−\frac{\mathrm{1}+{i}}{\mathrm{2}}\:\:\:{find}\:{lim}\:\mid{W}_{{n}} \mid\left({n}\rightarrow+\infty\right) \\ $$…