Question Number 128424 by bramlexs22 last updated on 07/Jan/21 $$\mathrm{If}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{is}\:\mathrm{an}\:\mathrm{even}\:\mathrm{function}\:\mathrm{and} \\ $$$$\mathrm{satisfies}\:\mathrm{the}\:\mathrm{relation}\:\mathrm{x}^{\mathrm{2}} \mathrm{f}\left(\mathrm{x}\right)−\mathrm{2f}\left(\mathrm{x}\right)=\mathrm{g}\left(\mathrm{x}\right) \\ $$$$\mathrm{where}\:\mathrm{g}\left(\mathrm{x}\right)\:\mathrm{is}\:\mathrm{an}\:\mathrm{odd}\:\mathrm{function}\: \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{5}\right)\:\mathrm{is}\: \\ $$$$\left(\mathrm{a}\right)\:\mathrm{0}\:\:\left(\mathrm{b}\right)\:\frac{\mathrm{37}}{\mathrm{75}}\:\:\:\left(\mathrm{c}\right)\:\mathrm{4}\:\:\:\:\left(\mathrm{d}\right)\:\frac{\mathrm{51}}{\mathrm{77}} \\ $$ Answered by mr W…
Question Number 62882 by mathmax by abdo last updated on 26/Jun/19 $${let}\:{f}\left({x}\right)={ln}\mid\frac{{x}−\mathrm{1}}{{x}+\mathrm{1}}\mid \\ $$$$\left.\mathrm{1}\right){determine}\:{D}_{{f}} \\ $$$$\left.\mathrm{2}\right)\:{calculatef}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{3}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\int_{−\frac{\mathrm{1}}{\mathrm{2}}} ^{\frac{\mathrm{1}}{\mathrm{2}}} {f}\left({x}\right){dx}\:. \\…
Question Number 62878 by mathmax by abdo last updated on 26/Jun/19 $${calculate}\:{min}\:\sum_{\mathrm{0}\leqslant{i}\leqslant{n}\:{and}\:\mathrm{0}\leqslant{j}\leqslant{n}} \:\:\:\:{i}.{j} \\ $$ Answered by mr W last updated on 26/Jun/19 $$\sum_{\mathrm{0}\leqslant{i}\leqslant{n}\:{and}\:\mathrm{0}\leqslant{j}\leqslant{n}} \:\:\:\:{i}.{j}…
Question Number 62879 by mathmax by abdo last updated on 26/Jun/19 $${calculate}\:{min}\:\sum_{\mathrm{0}\leqslant{i}\leqslant{n}\:\:{and}\:\mathrm{0}\leqslant{j}\leqslant{n}} \:\left({i}+{j}\right) \\ $$ Answered by mr W last updated on 26/Jun/19 $$\sum_{\mathrm{0}\leqslant{i}\leqslant{n}\:\:{and}\:\mathrm{0}\leqslant{j}\leqslant{n}} \:\left({i}+{j}\right)…
Question Number 62877 by mathmax by abdo last updated on 26/Jun/19 $${calculate}\:{lim}_{{n}\rightarrow+\infty} \:\sum_{{k}=\mathrm{0}} ^{\mathrm{2}{n}+\mathrm{1}} \:\frac{{n}}{{n}^{\mathrm{2}} \:+{k}} \\ $$ Commented by mathmax by abdo last updated…
Question Number 128401 by bramlexs22 last updated on 07/Jan/21 $$\mathrm{Given}\:\mathrm{function}\:\mathrm{f}\left({x}+\mathrm{1}\right)+\mathrm{f}\left({x}−\mathrm{1}\right)={x}^{\mathrm{2}} \\ $$$$\mathrm{then}\:\mathrm{f}^{−\mathrm{1}} \left({x}\right)\:=\:? \\ $$$$\left({A}\right)\:\pm\sqrt{\mathrm{1}−\mathrm{2}{x}}\:;\:{x}\leqslant\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\left({B}\right)\:\pm\sqrt{{x}+\mathrm{2}}\:;\:{x}\geqslant−\mathrm{2} \\ $$$$\left({C}\right)\:\pm\sqrt{\mathrm{2}{x}+\mathrm{1}}\:;\:{x}\geqslant−\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\left({D}\right)\:\pm\sqrt{\mathrm{3}{x}−\mathrm{1}}\:;\:{x}\geqslant\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\left({E}\right)\:\pm\sqrt{\mathrm{2}{x}−\mathrm{1}}\:;\:{x}\geqslant\frac{\mathrm{1}}{\mathrm{2}} \\ $$…
Question Number 128402 by bramlexs22 last updated on 07/Jan/21 $$\:\mathrm{If}\:\mathrm{f}\left({x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{4}\right)={x}+\mathrm{3}\:\mathrm{then}\:\mathrm{f}\left(−\mathrm{2}\right)=? \\ $$ Answered by liberty last updated on 07/Jan/21 $$\Rightarrow\mathrm{x}^{\mathrm{2}} −\mathrm{5x}+\mathrm{4}=−\mathrm{2}\:;\:\mathrm{x}^{\mathrm{2}} −\mathrm{5x}+\mathrm{6}=\mathrm{0} \\ $$$$\:\left(\mathrm{x}−\mathrm{3}\right)\left(\mathrm{x}−\mathrm{2}\right)=\mathrm{0}\:\rightarrow\begin{cases}{\mathrm{x}=\mathrm{3}}\\{\mathrm{x}=\mathrm{2}}\end{cases}\:\Leftrightarrow\mathrm{f}\left(−\mathrm{2}\right)=\begin{cases}{\mathrm{6}}\\{\mathrm{5}}\end{cases}…
Question Number 62815 by mathmax by abdo last updated on 25/Jun/19 $${developp}\:{at}\:{fourier}\:{serie}\:{f}\left({x}\right)\:={cos}\left({tx}\right)\:\:,\mathrm{2}\pi\:{periodic}\:{even}\:. \\ $$ Commented by mathmax by abdo last updated on 28/Jun/19 $${f}\:{is}\:{even}\:\Rightarrow{f}\left({x}\right)\:=\frac{{a}_{\mathrm{0}} }{\mathrm{2}}\:+\sum_{{n}=\mathrm{1}}…
Question Number 62777 by James Bryan Botshabelo last updated on 25/Jun/19 $$\mathrm{5}^{\mathrm{3}{x}−\mathrm{1}} .\mathrm{4}^{\mathrm{2}{x}−\mathrm{2}} =\mathrm{625} \\ $$ Commented by kaivan.ahmadi last updated on 25/Jun/19 $$\mathrm{5}^{\mathrm{2}{x}−\mathrm{1}} .\mathrm{5}^{{x}}…
Question Number 128176 by liberty last updated on 05/Jan/21 $$\mathrm{Given}\:\mathrm{t}\left(\mathrm{x}\right)=\mathrm{ax}^{\mathrm{4}} +\mathrm{bx}^{\mathrm{2}} +\mathrm{x}+\mathrm{5}\:;\:\mathrm{where}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b} \\ $$$$\mathrm{are}\:\mathrm{constant}.\:\mathrm{If}\:\mathrm{t}\left(−\mathrm{4}\right)=\mathrm{3}\:\mathrm{then}\:\mathrm{t}\left(\mathrm{4}\right)=? \\ $$ Answered by bemath last updated on 05/Jan/21 $$\left(\Rightarrow\right)\:\mathrm{t}\left(\mathrm{x}\right)=\mathrm{ax}^{\mathrm{4}} +\mathrm{bx}^{\mathrm{2}}…