Category: Relation and Functions

Question Number 97622 by mathmax by abdo last updated on 08/Jun/20 $$\mathrm{let}\mathrm{f}\left(\mathrm{x}\right)=\arctan ({\mathrm{x}}^2-3)$$$$1)\mathrm{calculate}{\mathrm{f}}^{\left(\mathrm{n}\right)}\left(\mathrm{x}\right)\mathrm{and}{\mathrm{f}}^{\left(\mathrm{n}\right)}\left(0\right)$$$$2)\mathrm{developp}\mathrm{f}\mathrm{at}\mathrm{integr}\mathrm{serie}$$$$3)\mathrm{calculate}{\int }_0^1\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}$$…

Question Number 97617 by mathmax by abdo last updated on 08/Jun/20 $$\mathrm{give}{\int }_0^{\mathrm{\infty }}\frac{\arctan \left(2\mathrm{x}\right)}{{(1+{\mathrm{x}}^2)}^2}\mathrm{dx}\mathrm{at}\mathrm{form}\mathrm{of}\mathrm{serie}$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 32042 by abdo imad last updated on 18/Mar/18 $$let{u}_n={\int }_0^1{x}^{n}sin\left(\pi x\right)dx$$$$1)provethat\mathrm{\Sigma }{u}_{n}converges$$$$2)provethat\mathrm{\Sigma }{u}_n={\int }_0^{\pi }\frac{sint}{t}dt.$$…

Question Number 32037 by abdo imad last updated on 18/Mar/18 $$let{u}_n=cos\left(\pi \sqrt{n^2+n+1}\right)findnatureof\mathrm{\Sigma }{u}_n.$$$$$$ Commented by abdo imad last updated on…

Question Number 32033 by abdo imad last updated on 18/Mar/18 $$letconsiderthesequence\left(u_n\right)/u_0\in [0,1]and$$$$\mathrm{\forall }n\in N{u}_{n+1}=u_n-u_n^2$$$$1)giveasimpleequivalentof{u}_n$$$$2)findthenatureof\mathrm{\Sigma }{u}_n.$$…