Category: Relation and Functions

Question Number 109191 by abdomsup last updated on 21/Aug/20 $$find{lim}_{x\to \frac{\pi }{2}}{\left(sinx\right)}^{ln\mid x-\frac{\pi }{2}\mid }$$ Commented by bemath last updated on 22/Aug/20 $$setx=\frac{\pi }{2}+z$$$${L}=\:\underset{{z}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\mathrm{sin}\:\left(\frac{\pi}{\mathrm{2}}+{z}\right)\right)^{\mathrm{ln}\:\mid{z}\mid} =\underset{{z}\rightarrow\mathrm{0}}…

Question Number 43541 by abdo.msup.com last updated on 11/Sep/18 $$let{u}_0=u_1=1and{u}_{n+1}=u_n+u_{n-1}$$$$2)find{u}_n$$$$3)let{x}_{0}thepositifrootsof{x}^2=x+1$$$$\left.\mathrm{4}\right)\:{prove}\:{that}\:\forall{n}\geqslant\mathrm{2}\:\:{x}_{\mathrm{0}} ^{{n}−\mathrm{2}} \leqslant{u}_{{n}} \leqslant{x}_{\mathrm{0}}…

Question Number 174570 by blackmamba last updated on 04/Aug/22 $$\{\begin{array}{l}\mathit{f}\left(\frac{\mathit{x}}{{\mathit{x}}^2+1}\right)=\frac{{\mathit{x}}^2}{{\mathit{x}}^4+2{\mathit{x}}^2+1}\\ \mathit{f}\left(\sqrt{3}\right)=?\end{array}$$ Commented by infinityaction last updated on 04/Aug/22 $$\:\:\:{f}\left(\frac{\mathrm{1}}{{x}+\frac{\mathrm{1}}{{x}}}\right)\:=\:\frac{\mathrm{1}}{\left({x}+\frac{\mathrm{1}}{{x}}\right)^{\mathrm{2}} }…

Question Number 108888 by bemath last updated on 20/Aug/20 $$\frac{⋮\mathcal{B}e\mathcal{M}ath⋮}{△}$$$$Suppose2x^3+3x^2-14x-5=(Px+Q)(x+3)(x+1)+Rforall$$$$valueofx.FindthevalueofP,QandR$$ Answered by Rasheed.Sindhi last updated on 20/Aug/20…

Question Number 43259 by maxmathsup by imad last updated on 08/Sep/18 $$calculate\sum _{n=2}^{\mathrm{\infty }}\frac{{(-1)}^n}{n^2-1}$$ Commented by maxmathsup by imad last updated…