Category: Relation and Functions

Question Number 45080 by turbo msup by abdo last updated on 08/Oct/18 $$find\sum _{n=0}^{\mathrm{\infty }}\frac{1}{{(2n+1)}^4}$$ Commented by maxmathsup by imad last updated…

Question Number 110449 by mathmax by abdo last updated on 29/Aug/20 $$\mathrm{find}{\lim }_{\mathrm{x}\to 0}\frac{\arctan (\mathrm{x}-\mathrm{sinx})-\arctan (1-\mathrm{cosx})}{{\mathrm{x}}^2}$$ Answered by bemath last updated on 29/Aug/20 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{x}−\mathrm{sin}\:\mathrm{x}−\left(\mathrm{1}−\mathrm{cos}\:\mathrm{x}\right)}{\mathrm{x}^{\mathrm{2}}…

Question Number 110306 by Lekhraj last updated on 28/Aug/20 Commented by mr W last updated on 28/Aug/20 $$f\left(x\right)=\frac{1\pm \sqrt{5}}{2}x$$ Commented by Lekhraj last updated…

Question Number 175801 by Lekhraj last updated on 07/Sep/22 $$solvethefollwingequation$$$$x\sqrt{x}+y\sqrt{y}=3andx\sqrt{y}+y\sqrt{x}=2$$$$someonesolvetheaboveequationsinthefollowingway$$$$x^3+y^3+2xy\sqrt{xy}=9\dots ..\left(1\right)and{x}^{2}y+y^{2}x+2xy\sqrt{xy}=4\dots \dots \left(2\right)$$$$\left(\mathrm{1}\right)\:−\:\left(\mathrm{2}\right)\:\:\:\Rightarrow\:\:\left({x}\:−\:{y}\right)\left({x}^{\mathrm{2}} \:−\:{y}^{\mathrm{2}} \:\right)\:=\:\mathrm{5} \…

Question Number 175674 by infinityaction last updated on 05/Sep/22 Answered by mr W last updated on 05/Sep/22 $$-\frac{b}{2a}=2\Rightarrow b=-4a$$$$f\left(2\right)=4a+2b+c=c-4a$$$$f\left(1\right)=a+b+c=c-3a=f\left(3\right)$$$${f}\left({f}\left(\mathrm{1}\right)\right)={f}\left({f}\left(\mathrm{2}\right)\right) \…