Question Number 51996 by maxmathsup by imad last updated on 01/Jan/19 $${calculate}\:{S}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:{sin}\left(\frac{\pi}{\mathrm{4}{n}}\:+\frac{{k}\pi}{\mathrm{2}{n}}\right)\: \\ $$$$ \\ $$ Commented by Abdo msup. last updated…
Question Number 51986 by maxmathsup by imad last updated on 01/Jan/19 $$\left.\mathrm{1}\right)\:{prove}\:{that}\:{thx}\:=\frac{\mathrm{2}}{{th}\left(\mathrm{2}{x}\right)}\:−\frac{\mathrm{1}}{{th}\left({x}\right)} \\ $$$$\left.\mathrm{2}\right){simplify}\:\:{S}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:\mathrm{2}^{{k}} {th}\left(\mathrm{2}^{{k}} {x}\right) \\ $$ Terms of Service Privacy…
Question Number 51985 by maxmathsup by imad last updated on 01/Jan/19 $$\left.\mathrm{1}\right)\:{let}\:{p}\:{integr}\:{natural}\:{not}\:\mathrm{0}\:{calculate}\:{arctan}\left(\frac{{p}}{{p}+\mathrm{1}}\right)−{arctan}\left(\frac{{p}−\mathrm{1}}{{p}}\right) \\ $$$$\left.\mathrm{2}\right){let}\:{S}_{{n}} =\sum_{{p}=\mathrm{1}} ^{{n}} \:{arctan}\left(\frac{\mathrm{1}}{\mathrm{2}{p}^{\mathrm{2}} }\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{S}_{{n}} \\ $$ Commented by Abdo msup.…
Question Number 51984 by maxmathsup by imad last updated on 01/Jan/19 $$\left.\mathrm{1}\right)\:{prove}\:{the}\:{convexity}\:{of}\:{f}\left({x}\right)={ln}\left(\mathrm{1}+{e}^{{x}} \right) \\ $$$$\left.\mathrm{2}\right)\:{prove}\:{that}\:\forall\left({x}_{\mathrm{1}} ,{x}_{\mathrm{2}} ,…,{x}_{{n}} \right)\in{R}^{{n}} \\ $$$$\mathrm{1}+\prod_{{k}=\mathrm{1}} ^{{n}} \left({x}_{{k}} \right)^{\frac{\mathrm{1}}{{n}}} \:\leqslant\:\prod_{{k}=\mathrm{1}} ^{{n}}…
Question Number 117518 by bobhans last updated on 12/Oct/20 $$\mathrm{f}\left(\mathrm{x}+\mathrm{1}\right)+\mathrm{xf}\left(\mathrm{1}−\mathrm{x}\right)=\mathrm{x}^{\mathrm{2}} \\ $$$$\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right)\:=? \\ $$ Answered by bemath last updated on 12/Oct/20 $$\mathrm{replace}\:\mathrm{x}+\mathrm{1}\:\mathrm{by}\:\mathrm{x} \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{f}\left(\mathrm{x}\right)+\left(\mathrm{x}−\mathrm{1}\right)\mathrm{f}\left(\mathrm{1}−\left(\mathrm{x}−\mathrm{1}\right)\right)=\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{2}}…
Question Number 51982 by maxmathsup by imad last updated on 01/Jan/19 $${let}\:{u}_{{n}+\mathrm{1}} =\sqrt{\sum_{{k}=\mathrm{1}} ^{{n}} \:{u}_{{k}} }\:\:\:\:\:\:\:{with}\:{n}>\mathrm{0}\:\:\:{and}\:{u}_{\mathrm{1}} =\mathrm{1} \\ $$$$\left.\mathrm{1}\right){calculate}\:{u}_{\mathrm{2}} ,{u}_{\mathrm{3}} ,{u}_{\mathrm{4}} {and}\:{u}_{\mathrm{5}} \\ $$$$\left.\mathrm{2}\right){prove}\:{that}\:\:\forall{n}\geqslant\mathrm{2}\:\:\:\:\:{u}_{{n}+} ^{\mathrm{2}}…
Question Number 51983 by maxmathsup by imad last updated on 01/Jan/19 $${f}\:{is}\:{a}\:{real}\:{function}\:{derivable}\:{at}\:\mathrm{0}\:{and}\:{f}\left(\mathrm{0}\right)=\mathrm{0}\:{find} \\ $$$${lim}_{{n}\rightarrow+\infty} \sum_{{k}=\mathrm{1}} ^{{n}} \:{f}\left(\frac{{k}}{{n}^{\mathrm{2}} }\right)\:. \\ $$ Terms of Service Privacy Policy…
Question Number 51981 by maxmathsup by imad last updated on 01/Jan/19 $${let}\:\:{U}_{{n}} =\:\frac{\sum_{{k}=\mathrm{1}} ^{{n}} \left[{lnk}\right]}{{ln}\left({n}!\right)}\:\:{determine}\:{lim}_{{n}\rightarrow+\infty} \:{U}_{{n}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 117508 by bemath last updated on 12/Oct/20 $$\mathrm{f}\left(\mathrm{x}+\mathrm{1}\right)+\mathrm{f}\left(\mathrm{x}−\mathrm{1}\right)\:=\:\mathrm{x}^{\mathrm{2}} \: \\ $$$$\mathrm{find}\:\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right)\:=? \\ $$ Answered by bobhans last updated on 12/Oct/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}+\mathrm{c}…
Question Number 51720 by Tawa1 last updated on 29/Dec/18 Terms of Service Privacy Policy Contact: info@tinkutara.com