Question Number 36929 by maxmathsup by imad last updated on 07/Jun/18 $${study}\:{and}\:{give}\:{th}\:{graph}\:{of}\:{the}\:{function} \\ $$$${f}\left({x}\right)={x}\left(\mathrm{1}−\frac{\mathrm{1}}{{x}}\right)^{{x}+\mathrm{1}} . \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 36927 by maxmathsup by imad last updated on 07/Jun/18 $${f}\:{is}\:{a}\:{real}\:{function}\:{derivable}\:{on}\:\left[\mathrm{0},\mathrm{1}\right]\:/{f}\left(\mathrm{0}\right)=\mathrm{0}\:{and}\:{f}\left(\mathrm{1}\right)=\mathrm{1} \\ $$$${prove}\:{that}\:\forall{n}\in{N}\:\:\exists\:\:\:\left({x}_{{i}} \right)_{\mathrm{1}\leqslant{i}\leqslant{n}} \:{seqence}\:{of}\:{reals}\:{with}\:{x}_{{i}} \neq{x}_{{j}} \:{if}\:{i}\neq{j} \\ $$$${and}\:\sum_{{k}=\mathrm{1}} ^{{n}} \:{f}^{'} \left({x}_{{k}} \right)={n}. \\…
Question Number 36925 by maxmathsup by imad last updated on 07/Jun/18 $${find}\:{lim}_{{n}\rightarrow+\infty} \:\prod_{{k}=\mathrm{1}} ^{{n}} \:\:\left(\mathrm{1}+\frac{{k}}{{n}^{\mathrm{2}} }\right). \\ $$ Commented by math khazana by abdo last…
Question Number 36922 by maxmathsup by imad last updated on 07/Jun/18 $$\left({u}_{{n}} \right){is}\:{a}\:{sequence}\:{and}\:{lim}_{{n}\rightarrow+\infty} {u}_{{n}} ={l}\:{let} \\ $$$${v}_{{n}} =\:\frac{\mathrm{1}}{\mathrm{2}^{{n}} }\:\sum_{{k}=\mathrm{0}} ^{{n}} {C}_{{n}} ^{{k}} \:{u}_{{k}} \:\:{prove}\:{that}\:{v}_{{n}} \:\rightarrow{l}\left({n}\rightarrow+\infty\:\right)…
Question Number 36923 by maxmathsup by imad last updated on 07/Jun/18 $${for}\:{t}\geqslant\mathrm{0}\:{and}\:\:{f}\left({t}\right)=\:\frac{{t}}{\:\sqrt{\mathrm{1}+{t}}}\:\:{let} \\ $$$${S}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:{f}\left(\frac{{k}}{{n}^{\mathrm{2}} }\right)\:\:{study}\:{the}\:{convergence}\:{of}\:{S}_{{n}} \:\:. \\ $$ Commented by abdo.msup.com last…
Question Number 36924 by maxmathsup by imad last updated on 07/Jun/18 $${calculate}\:\:{lim}_{{n}\rightarrow+\infty} \:\:\frac{\mathrm{1}}{\mathrm{2}{i}}\left\{\:\left(\mathrm{1}+\frac{{it}}{{n}}\right)^{{n}} \:−\left(\mathrm{1}−\frac{{it}}{{n}}\right)^{{n}} \right) \\ $$ Commented by math khazana by abdo last updated…
Question Number 36921 by maxmathsup by imad last updated on 07/Jun/18 $${study}\:{the}\:{convergence}\:{of}\:\:{u}_{\mathrm{1}} ={ln}\left(\mathrm{2}\right)\:{and}\:{u}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}−\mathrm{1}} {ln}\left(\mathrm{2}−{u}_{{k}} \right). \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 36920 by maxmathsup by imad last updated on 07/Jun/18 $${let}\:\alpha\:{from}\:{R}\:{and}\:\:{u}_{{n}} \:−\mathrm{2}{cos}\left(\alpha\right){u}_{{n}−\mathrm{1}} \:+{u}_{{n}−\mathrm{2}} =\mathrm{0}\:\:\:{withn}\geqslant\mathrm{2} \\ $$$${find}\:{u}_{{n}} \:{and}\:{study}\:{its}\:{convrgence}. \\ $$ Commented by math khazana by…
Question Number 36908 by prof Abdo imad last updated on 07/Jun/18 $${calculate}\:{S}_{{n}} =\:\sum_{{p}=\mathrm{1}} ^{{n}} \:\:\frac{{p}}{\mathrm{1}+{p}\:+{p}^{\mathrm{2}} } \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+} \:{S}_{{n}} \:\:. \\ $$ Terms of Service…
Question Number 36820 by maxmathsup by imad last updated on 06/Jun/18 $${find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{2}} ^{\infty} \:\:\frac{\mathrm{1}}{\left({n}−\mathrm{1}\right)^{\mathrm{2}} \left({n}+\mathrm{1}\right)^{\mathrm{2}} }\: \\ $$ Commented by math khazana by abdo last…