Question Number 130064 by mathmax by abdo last updated on 22/Jan/21 $$\mathrm{let}\:\mathrm{A}_{\mathrm{n}} =\begin{pmatrix}{\mathrm{cos}\left(\frac{\mathrm{n}\pi}{\mathrm{3}}\right)\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{sin}\left(\frac{\mathrm{n}\pi}{\mathrm{3}}\right)}\\{\mathrm{sin}\left(\frac{\mathrm{n}\pi}{\mathrm{3}}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{cos}\left(\frac{\mathrm{n}\pi}{\mathrm{3}}\right)}\end{pmatrix} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{calculate}\:\mathrm{A}_{\mathrm{0}} ,\mathrm{A}_{\mathrm{1}} \:\mathrm{and}\:\mathrm{A}_{\mathrm{2}} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{calculate}\:\mathrm{det}\left(\mathrm{A}_{\mathrm{n}} \right)\:\mathrm{is}\:\mathrm{A}_{\mathrm{n}} \mathrm{inversible}? \\ $$$$\left.\mathrm{3}\right)\:\mathrm{calculste}\:\mathrm{A}_{\mathrm{n}} ^{\mathrm{n}} \\…
Question Number 64444 by mathmax by abdo last updated on 18/Jul/19 $${calculate}\:{A}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:\frac{{k}}{\left({k}+\mathrm{1}\right)!} \\ $$ Commented by Prithwish sen last updated on 18/Jul/19…
Question Number 64445 by mathmax by abdo last updated on 18/Jul/19 $${calculate}\:\:{W}_{{n}} =\sum_{\mathrm{1}\leqslant{i}\leqslant{j}\leqslant{n}} \:{i}×{j} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 64443 by mathmax by abdo last updated on 18/Jul/19 $${find}\:{all}\:{functin}\:{f}\:{Z}\rightarrow{Z}\:\:{wich}\:{verify} \\ $$$$\forall\left({a},{b}\right)\in{Z}^{\mathrm{2}} \:\:\:\:\:{f}\left(\mathrm{2}{a}\right)+\mathrm{2}{f}\left({b}\right)\:={f}\left({f}\left({a}+{b}\right)\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 64355 by turbo msup by abdo last updated on 17/Jul/19 $${let}\:{F}\left({x}\right)=\int_{{u}\left({x}\right)} ^{{v}\left({x}\left\{\right.\right.} {f}\left({x},{t}\right){dt} \\ $$$${how}\:{to}\:{calculate}\:\:\frac{{dF}}{{dx}}\left({x}\right)? \\ $$ Commented by MJS last updated on…
Question Number 129873 by Bird last updated on 20/Jan/21 $${let}\:{m}={inff}\left({x}\right)_{{x}\in\left[{a},{b}\right]} \\ $$$${and}\:{M}={supf}\left({x}\right)_{{x}\in\left[{a},{b}\right]} \\ $$$${prove}\:{that}\:\left({b}−{a}\right)^{\mathrm{2}} \leqslant\int_{{a}} ^{{b}} {f}\left({x}\right){dx}.\int_{{a}} ^{{b}} \:\frac{{dx}}{{f}\left({x}\right)} \\ $$$$\leqslant\left({b}−{a}\right)^{\mathrm{2}} ×\frac{\left({m}+{M}\right)^{\mathrm{2}} }{\mathrm{4}{mM}} \\ $$…
Question Number 129872 by Bird last updated on 20/Jan/21 $${let}\:{S}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{{n}−{k}}{{n}^{\mathrm{2}} \:+{nk}+\mathrm{2009}} \\ $$$${determine}\:{lim}_{{n}\rightarrow+\infty} \:{S}_{{n}} \\ $$ Answered by Dwaipayan Shikari last updated…
Question Number 129870 by Bird last updated on 20/Jan/21 $${f}\:{continue}\:{on}\:\left[\bar {\mathrm{0}1}\right]\:{calculate} \\ $$$${lim}_{{n}\rightarrow+\infty} \frac{\mathrm{1}}{{n}}\sum_{{k}=\mathrm{0}} ^{{n}} \left({n}−{k}\right)\int_{\frac{{k}}{{n}}} ^{\frac{{k}+\mathrm{1}}{{n}}} {f}\left({x}\right){dx} \\ $$ Terms of Service Privacy Policy…
Question Number 129869 by Bird last updated on 20/Jan/21 $${calculate}\:{lim}_{{n}\rightarrow+\infty} \sum_{{k}=\mathrm{1}} ^{{n}} \frac{\mathrm{1}}{\left.\:\sqrt{\left({k}+{n}\right)\left({k}+\mathrm{1}+{n}\right.}\right)} \\ $$ 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}…
Question Number 64300 by mathmax by abdo last updated on 16/Jul/19 Terms of Service Privacy Policy Contact: info@tinkutara.com