Question Number 38024 by Tinkutara last updated on 20/Jun/18 Answered by ajfour last updated on 20/Jun/18 $${f}\left({x}\right)\:<\:\mathrm{0}\:\:{and} \\ $$$$\mathrm{2}{f}\left(\mathrm{sin}\:{x}\right)+\sqrt{\mathrm{2}}{f}\left(−\mathrm{cos}\:{x}\right)=−\mathrm{tan}\:{x} \\ $$$${Then}\:\:{for}\:{x}=\mathrm{150}° \\ $$$$\mathrm{2}{f}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)+\sqrt{\mathrm{2}}{f}\left(\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\right)=\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}\:\:\:……\left({i}\right) \\ $$$${for}\:{x}=\:\mathrm{120}°…
Question Number 103458 by bobhans last updated on 15/Jul/20 $$\left(\mathrm{1}\right){If}\:{p}\:{and}\:{q}\:{are}\:{the}\:{roots}\:{quadratic} \\ $$$${equation}\:{x}^{\mathrm{2}} −{x}−\mathrm{4050}\:=\:\mathrm{0}\:,\:{find}\:{the}\:{value} \\ $$$${of}\:{p}^{\mathrm{2}} +{q}\:?\: \\ $$$$\left(\mathrm{2}\right)\:{if}\:{f}\left({x}\right)=\frac{\mathrm{7}{x}+{q}}{\mathrm{2}}\:{and}\:{g}\left({x}\right)=\mathrm{7}{x}+\mathrm{8}\:; \\ $$$$\left({fog}\right)\left(\mathrm{4}\right)\:=\:\mathrm{24}\:.\:{find}\:{the}\:{value}\:{of}\:{q} \\ $$ Answered by bemath…
Question Number 103457 by bobhans last updated on 15/Jul/20 $${f}\left(\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}\right)\:=\:{x}+\mathrm{2}\:{then}\:{what}\:{is}\:{the}\:{domain} \\ $$$${and}\:{range}\:{of}\:{f}^{−\mathrm{1}} \left({x}\right)\:? \\ $$ Answered by Worm_Tail last updated on 15/Jul/20 $$\:\:\:{f}\left(\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}\right)={x}+\mathrm{2} \\ $$$$\:\:\:\left(\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}\right)={f}^{−\mathrm{1}}…
Question Number 37901 by math khazana by abdo last updated on 19/Jun/18 $${let}\:{f}\left({x}\right)=\:\left(\mathrm{1}+{e}^{−{x}} \right)^{{n}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({p}\right)} \left({x}\right)\:\:{and}\:{f}^{\left({p}\right)} \left({o}\right) \\ $$$$\left.\mathrm{2}\right){calculate}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{3}\right){developp}\:{f}\:{at}\:{integr}\:{serie}\:. \\ $$…
Question Number 37894 by abdo mathsup 649 cc last updated on 19/Jun/18 $${find}\:{nature}\:{of}\:{the}\:{serie} \\ $$$$\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\left(\sum_{{k}=\mathrm{0}} ^{{n}} \:\:\frac{\mathrm{1}}{{C}_{{n}} ^{{k}} }\right){x}^{{n}} \\ $$ Terms of…
Question Number 37891 by abdo mathsup 649 cc last updated on 19/Jun/18 $${calculate}\:{B}_{{n}} =\:\sum_{{k}=\mathrm{0}} ^{{n}} \:\left(−\mathrm{1}\right)^{{k}} \left(\mathrm{2}{k}^{\mathrm{2}} \:+\mathrm{1}\right)\:{interms}\:{of}\:{n}. \\ $$ Commented by prof Abdo imad…
Question Number 37892 by abdo mathsup 649 cc last updated on 19/Jun/18 $${let}\:\:\:{f}\left({x}\right)=\sqrt{{x}+\sqrt{{x}+\mathrm{1}}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:\:{D}_{{f}} \\ $$$$\left.\mathrm{2}\right)\:\:{give}\:{the}\:{equation}\:{of}\:{assymtote}\:{at}\:{point} \\ $$$${A}\left(\mathrm{0},{f}\left({o}\right)\right) \\ $$$$\left.\mathrm{3}\right)\:{if}\:{f}\left({x}\right)\sim\:{a}\left({x}−\mathrm{1}\right)\:\:+{b}\:\:\left({x}\rightarrow\mathrm{1}\right)\:{determine}\:{a}\:{andb} \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:{f}^{'} \left({x}\right) \\…
Question Number 103412 by abdomsup last updated on 14/Jul/20 $${solve}\:\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} {y}^{''} \:+\mathrm{2}{x}\left(\mathrm{1}+{x}^{\mathrm{2}} \right){y}^{'} \:+\mathrm{2}=\mathrm{0} \\ $$ Answered by OlafThorendsen last updated on 15/Jul/20 $$\left(\mathrm{1}+{x}^{\mathrm{2}}…
Question Number 103411 by abdomsup last updated on 14/Jul/20 $${solve}\:{x}^{\mathrm{2}} {y}^{''} \:+{xy}^{'} \:+{y}\:=\mathrm{0} \\ $$ Answered by bemath last updated on 14/Jul/20 $${set}\:{y}={x}^{{r}} \\ $$$${y}'={rx}^{{r}−\mathrm{1}}…
Question Number 37818 by prof Abdo imad last updated on 17/Jun/18 $${let}\:\mathrm{0}<{u}_{\mathrm{0}} <\mathrm{1}\:\:{and}\:{u}_{{n}+\mathrm{1}} =\sqrt{\frac{\mathrm{1}+{u}_{{n}} }{\mathrm{2}}} \\ $$$${study}\:{the}\:{convergence}\:{of}\:{u}_{{n}} \: \\ $$$$ \\ $$ Commented by math…