Question Number 27618 by NECx last updated on 11/Jan/18 $${Find}\:{the}\:{range}\:{of}\:{y}={x}\left({x}^{\mathrm{6}} −\mathrm{1}\right).{For} \\ $$$${which}\:{y}=\mathrm{0} \\ $$ Answered by mrW2 last updated on 13/Jan/18 $${y}={x}\left({x}^{\mathrm{6}} −\mathrm{1}\right)=\mathrm{0} \\…
Question Number 158668 by cortano last updated on 07/Nov/21 $$\:{f}\left({f}\left({x}\right)\right)=\:\left(\mathrm{9}{x}^{\mathrm{2}} +\mathrm{6}{x}+\mathrm{2}\right){f}\left({x}\right) \\ $$$$\:{f}\left({x}\right)=? \\ $$ Answered by ajfour last updated on 07/Nov/21 $${Assuming}\:{f}\left({x}\right)\:{is}\:{a}\:{polynome}.. \\ $$$${n}^{\mathrm{2}}…
Question Number 92933 by mathmax by abdo last updated on 09/May/20 $${prove}\:{thst}\:{for}\:{z}\in{C}−{Z}\:\:\:\:\:\left(\frac{\pi{z}}{{sin}\left(\pi{z}\right)}\right)^{\mathrm{2}} \:=\sum_{{n}=−\infty} ^{+\infty} \:\frac{\mathrm{1}}{\left({z}−{n}\right)^{\mathrm{2}} } \\ $$$${and}\:\:\frac{\left(\pi{z}\right)^{\mathrm{2}} }{{sin}^{\mathrm{2}} \left(\pi{z}\right)}{cos}\left(\pi{z}\right)\:=\sum_{{n}=−\infty} ^{+\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}} }{\left({z}−{n}\right)^{\mathrm{2}} } \\…
Question Number 27379 by abdo imad last updated on 05/Jan/18 $${let}\:{give}\:{f}\left({x}\right)=\:\:\int_{{x}} ^{\mathrm{2}{x}} \:\:\frac{{dt}}{{ln}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)}\:\:{calculate}\:{f}^{'} \left({x}\right). \\ $$ Commented by abdo imad last updated on 05/Jan/18…
Question Number 158334 by alcohol last updated on 02/Nov/21 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{{x}}\underset{{r}=\mathrm{1}} {\overset{{x}} {\sum}}{cos}\left(\frac{{r}\pi}{\mathrm{2}{x}}\right) \\ $$$${x}\in\mathbb{N} \\ $$ Commented by aleks041103 last updated on 02/Nov/21 $${The}\:{upper}\:{bound}\:{of}\:{the}\:{summation}…
Question Number 158306 by mathlove last updated on 02/Nov/21 Commented by cortano last updated on 02/Nov/21 $${f}\left(\mathrm{1}−{x}\right)=\frac{\mathrm{4}^{\mathrm{1}−{x}} }{\mathrm{4}^{\mathrm{1}−{x}} +\mathrm{2}}\:=\:\frac{\frac{\mathrm{4}}{\mathrm{4}^{{x}} }}{\frac{\mathrm{4}}{\mathrm{4}^{{x}} }+\mathrm{2}}=\frac{\mathrm{4}}{\mathrm{4}+\mathrm{2}.\mathrm{4}^{{x}} } \\ $$$${f}\left({x}\right)+{f}\left(\mathrm{1}−{x}\right)=\frac{\mathrm{4}^{{x}} }{\mathrm{4}^{{x}}…
Question Number 92768 by mathmax by abdo last updated on 09/May/20 $${calculate}\:{A}_{{n}} =\:\sum_{{k}=\mathrm{0}} ^{{n}} \:{C}_{{n}} ^{{k}} \:{cos}^{\mathrm{3}} \left({kx}\right)\:\:{and}\:\sum_{{k}=\mathrm{0}} ^{{n}} \:{C}_{{n}} ^{{k}} \:{sin}^{\mathrm{3}} \left({kx}\right) \\ $$…
Question Number 92767 by mathmax by abdo last updated on 09/May/20 $${let}\:{U}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:{e}^{−{nx}} {cosx}\:{dx} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{lim}_{{n}\rightarrow+\infty} {n}^{\mathrm{2}} \:{U}_{{n}} \\ $$$$\left.\mathrm{2}\right){calculate}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{U}_{{n}} \\…
Question Number 92769 by mathmax by abdo last updated on 09/May/20 $${calculate}\:\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:{C}_{{n}} ^{{k}} \:{cos}^{\mathrm{2}} \left(\frac{{k}\pi}{{n}}\right)\:\:\:\:\:\left({n}\geqslant\mathrm{2}\right) \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 92763 by msup by abdo last updated on 09/May/20 $${study}\:{the}\:{sequence}\:{u}_{{n}+\mathrm{1}} =\sqrt{{u}_{{n}} ^{\mathrm{2}} +\frac{\mathrm{1}}{{n}}} \\ $$$${and}\:{u}_{\mathrm{1}} =\mathrm{1} \\ $$ Commented by i jagooll last…