Category: Relation and Functions

Question Number 33699 by math khazana by abdo last updated on 22/Apr/18 $$letS\left(x\right)=\sum _{n=0}^{\mathrm{\infty }}{f}_n\left(x\right)with{f}_n\left(x\right)=\frac{{(-1)}^n}{n!(x+n)}$$$$x\in ]0,+\mathrm{\infty }[$$$$1)provethatSiddefined.calculateS\left(1\right)and$$$${prove}\:{that}\:\forall{x}>\mathrm{0}\:\:{xS}\left({x}\right)\:−{S}\left({x}+\mathrm{1}\right)\:=\frac{\mathrm{1}}{{e}} \…

Question Number 99222 by mathmax by abdo last updated on 19/Jun/20 $$\mathrm{calculate}\sum _{\mathrm{n}=0}^{\mathrm{\infty }}\frac{{(-1)}^{\mathrm{n}}}{{(\mathrm{n}+1)}^2{(\mathrm{n}+2)}^3}$$ Terms of Service Privacy Policy Contact:…

Question Number 33651 by rahul 19 last updated on 21/Apr/18 $$Letfunctionf\left(x\right)bedefinedas$$$$f\left(x\right)=x^2+bx+c,whereb,c\in R.$$$$Andf\left(1\right)-2f\left(5\right)+f\left(9\right)=32.$$$$Findno.oforderedpairs(b,c)$$$$suchthat\mid f\left(x\right)\mid ⩽8\mathrm{\forall }x\in [1,9]?$$ Answered by MJS…

Question Number 99159 by bemath last updated on 19/Jun/20 Commented by som(math1967) last updated on 19/Jun/20 $$\mathrm{let}\mathrm{pt}.\mathrm{on}\mathrm{paabola}(\mathrm{h},\mathrm{k})$$$$\therefore \sqrt{{(\mathrm{h}+3)}^2+{(\mathrm{k}-3)}^2}=\frac{\mid \mathrm{k}-7\mid }{\sqrt{1^2}}$$$$\Rightarrow\left(\mathrm{h}+\mathrm{3}\right)^{\mathrm{2}} +\left(\mathrm{k}−\mathrm{3}\right)^{\mathrm{2}}…

Question Number 33596 by abdo imad last updated on 19/Apr/18 $$1)provethat\mathrm{\forall }(a,b)\in R^2\mid sinb-sina\mid ⩽\mid b-a\mid$$$$2)letgivethesequence{x}_0=0and$$$$x_{n+1}=a+\frac{1}{2}sin\left(x_n\right)provethatform⩾n$$$$\mid{x}_{{m}} \:−{x}_{{n}} \mid\:\leqslant\:\:\frac{\mid{a}\mid}{\mathrm{2}^{{n}−\mathrm{1}} } \…