Category: Relation and Functions

Question Number 130064 by mathmax by abdo last updated on 22/Jan/21 $$\mathrm{let}{\mathrm{A}}_{\mathrm{n}}=\left(\begin{array}{c}\cos \left(\frac{\mathrm{n}\pi }{3}\right)\sin \left(\frac{\mathrm{n}\pi }{3}\right)\\ \sin \left(\frac{\mathrm{n}\pi }{3}\right)\cos \left(\frac{\mathrm{n}\pi }{3}\right)\end{array}\right)$$$$1)\mathrm{calculate}{\mathrm{A}}_0,{\mathrm{A}}_1\mathrm{and}{\mathrm{A}}_2$$$$2)\mathrm{calculate}\det \left({\mathrm{A}}_{\mathrm{n}}\right)\mathrm{is}{\mathrm{A}}_{\mathrm{n}}\mathrm{inversible}?$$$$\left.\mathrm{3}\right)\:\mathrm{calculste}\:\mathrm{A}_{\mathrm{n}} ^{\mathrm{n}} \…

Question Number 64445 by mathmax by abdo last updated on 18/Jul/19 $$calculate{W}_n=\sum _{1⩽i⩽j⩽n}i\times j$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 64355 by turbo msup by abdo last updated on 17/Jul/19 $$letF\left(x\right)={\int }_{u\left(x\right)}^{v(x\{}f(x,t)dt$$$$howtocalculate\frac{dF}{dx}\left(x\right)?$$ Commented by MJS last updated on…

Question Number 129872 by Bird last updated on 20/Jan/21 $$let{S}_n=\sum _{k=1}^n\frac{n-k}{n^2+nk+2009}$$$$determine{lim}_{n\to +\mathrm{\infty }}{S}_n$$ Answered by Dwaipayan Shikari last updated…

Question Number 129869 by Bird last updated on 20/Jan/21 $$calculate{lim}_{n\to +\mathrm{\infty }}\sum _{k=1}^n\frac{1}{\sqrt{(k+n)(k+1+n})}$$ Answered by mindispower last updated on 20/Jan/21 $$$$$$\frac{\mathrm{1}}{\left({k}+\mathrm{1}+{n}\right)}\leqslant\frac{\mathrm{1}}{\:\sqrt{{k}+{n}}.\sqrt{{k}+\mathrm{1}+{n}}}\leqslant\frac{\mathrm{1}}{{k}+{n}}…\mathrm{1}…