Category: Relation and Functions

Question Number 48169 by Abdo msup. last updated on 20/Nov/18 $$let{u}_n={\int }_0^{\mathrm{\infty }}cos\left({nx}^2\right)dxand{v}_n={\int }_0^{\mathrm{\infty }}sin\left({nx}^2\right)dxwithn>0$$$$1)calculste{u}_{n}and{v}_n$$$$\left.\mathrm{2}\right){find}\:{nsture}\:{of}\:\Sigma\left({u}_{{n}} +\mathrm{2}{v}_{{n}}…

Question Number 48068 by maxmathsup by imad last updated on 18/Nov/18 $$let{u}_n={\int }_0^{\mathrm{\infty }}\frac{dt}{1+t^n}$$$$findnatureof\mathrm{\Sigma }{u}_{n}and\mathrm{\Sigma }\frac{u_n}{n^2}and\mathrm{\Sigma }\frac{u_n}{n^3}$$…

Question Number 113549 by mathmax by abdo last updated on 13/Sep/20 $$\mathrm{let}\mathrm{A}=\left(\begin{array}{c}1-\frac{1}{\mathrm{n}}\\ \frac{1}{\mathrm{n}}1\end{array}\right)$$$$1)\mathrm{calculate}{\mathrm{A}}^2$$$$2)\mathrm{calculate}{\mathrm{A}}^{\mathrm{m}}\left(\mathrm{m}\mathrm{integr}\mathrm{natural}\right)$$$$3)\mathrm{coclude}{\mathrm{A}}^{\mathrm{n}}\mathrm{and}{\lim }_{\mathrm{n}\to +\mathrm{\infty }}{\mathrm{A}}^{\mathrm{n}}$$$$\left.\mathrm{4}\right)\:\mathrm{calculate}\:\mathrm{e}^{\mathrm{A}} \:\mathrm{and}\:\mathrm{e}^{−\mathrm{A}} \…

Question Number 47857 by maxmathsup by imad last updated on 15/Nov/18 $$let{A}_n=\sum _{k=0}^{n-1}sin\left(\frac{k\pi }{2n}\right)and{B}_n=\sum _{k=0}^{n-1}cos\left(\frac{k\pi }{2n}\right)$$$$1)find{A}_{n}and{B}_{n}intermsofn$$$$\left.\mathrm{2}\right){calculate}\:{lim}_{{n}\rightarrow+\infty} \:\:\frac{{A}_{{n}}…

Question Number 178624 by infinityaction last updated on 19/Oct/22 $$\mathbf{let}\mathbf{f}:[0,1]\to \mathbb{R}\mathbf{be}\mathbf{given}\mathbf{by}$$$$\mathbf{f}\left(\mathbf{x}\right)=\frac{{(1+{\mathbf{x}}^{\frac{1}{3}})}^3+{(1-{\mathbf{x}}^{\frac{1}{3}})}^3}{8(1+\mathbf{x})}\mathbf{then}$$$$\mathbf{max}\{\mathbf{f}\left(\mathbf{x}\right):\mathbf{x}\in [0,1]\}-\mathbf{min}\{\mathbf{f}\left(\mathbf{x}\right):\mathbf{x}\in [0,1]\}$$$$\mathrm{is}$$ Answered by a.lgnaoui…