Question Number 57406 by Abdo msup. last updated on 03/Apr/19 $${let}\:{f}\left({x}\right)=\frac{{x}}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}\:+{cos}\left(\pi{x}\right) \\ $$$$\left.\mathrm{1}\left.\right)\:{prove}\:{that}\:{f}\left({x}\right)=\mathrm{0}\:{have}\:{a}\:{solurion}\:\alpha\:{inside}\:\right]\mathrm{0},\mathrm{1}\left[\right. \\ $$$$\left.\mathrm{2}\right)\:{use}\:{newton}\:{method}\:{to}\:{find}\:{a}\:{approximate}\: \\ $$$${value}\:{of}\:\alpha\:. \\ $$ Commented by kaivan.ahmadi last updated…
Question Number 57407 by Abdo msup. last updated on 03/Apr/19 $${let}\:{U}_{\mathrm{0}} ={cos}\left(\frac{\pi}{\mathrm{3}}\right)\:{and}\:{U}_{{n}+\mathrm{1}} =\sqrt{\frac{\mathrm{1}+{U}_{{n}} }{\mathrm{2}}} \\ $$$${find}\:{U}_{{n}} \:{interms}\:{of}\:{n}\:. \\ $$ Commented by Abdo msup. last updated…
Question Number 57389 by rahul 19 last updated on 03/Apr/19 $${If}\:{a}\epsilon{R}\:{and}\:{the}\:{equation}\:: \\ $$$$−\mathrm{3}\left\{{x}\right\}^{\mathrm{2}} +\mathrm{2}\left\{{x}\right\}+{a}^{\mathrm{2}} =\mathrm{0}\:{has}\:{no}\:{integral} \\ $$$${solution},\:{then}\:{all}\:{possible}\:{value}\:{of}\:{a} \\ $$$${lie}\:{in}\:{the}\:{interval}\:: \\ $$$$\left({a}\right)\left(−\mathrm{1},\mathrm{0}\right)\mathrm{U}\left(\mathrm{0},\mathrm{1}\right)\:\:\:\left({b}\right)\left(\mathrm{1},\mathrm{2}\right) \\ $$$$\left({c}\right)\:\left(−\mathrm{2},−\mathrm{1}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\left({d}\right)\left(−\infty,−\mathrm{2}\right)\mathrm{U}\left(\mathrm{2},\infty\right) \\ $$…
Question Number 122788 by 676597498 last updated on 19/Nov/20 Answered by mr W last updated on 20/Nov/20 $$\mathrm{0}<\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{1000}}<\mathrm{1}\Rightarrow\left[\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{1000}}\right]=\mathrm{0} \\ $$$$… \\ $$$$\mathrm{0}<\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{499}}{\mathrm{1000}}<\mathrm{1}\Rightarrow\left[\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{499}}{\mathrm{1000}}\right]=\mathrm{0} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{500}}{\mathrm{1000}}=\mathrm{1}\Rightarrow\left[\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{500}}{\mathrm{1000}}\right]=\mathrm{1} \\…
Question Number 57232 by maxmathsup by imad last updated on 31/Mar/19 $${decompose}\:{tbe}\:{fraction}\:{F}\left({x}\right)=\frac{\mathrm{1}}{{x}^{{n}} \left({x}+\mathrm{1}\right)}\:\:{with}\:{n}\:{integr}\:{natural}. \\ $$ Commented by maxmathsup by imad last updated on 14/Apr/19 $$\:{the}\:{dcomposition}\:{of}\:{F}\:{is}\:{F}\left({x}\right)\:=\frac{{a}}{{x}+\mathrm{1}}\:+\sum_{{i}=\mathrm{1}}…
Question Number 122615 by john santu last updated on 18/Nov/20 Commented by liberty last updated on 18/Nov/20 $$\:\frac{\mathrm{1}}{{t}}\:=\:\frac{\mathrm{1}}{\mathrm{12}}\:+\:\frac{\mathrm{1}}{\mathrm{15}}\:−\:\frac{\mathrm{1}}{\mathrm{10}}\:=\:\frac{\mathrm{5}+\mathrm{4}−\mathrm{6}}{\mathrm{60}}\: \\ $$$$\:\frac{\mathrm{1}}{{t}}\:=\:\frac{\mathrm{1}}{\mathrm{20}}\:\Rightarrow\:{t}\:=\:\mathrm{20}\:{hours} \\ $$ Terms of Service…
Question Number 57020 by 121194 last updated on 28/Mar/19 $$\left[{f}\left({x}+\mathrm{1}\right)−{f}\left({x}\right)\right]^{\mathrm{2}} =\mathrm{4}\left[{f}\left({x}\right)−\mathrm{1}\right] \\ $$$${f}\left({x}\right)=? \\ $$$$−−−−−−−−−−−−− \\ $$$${f}\left(\mathrm{0}\right)=\mathrm{0} \\ $$ Commented by kaivan.ahmadi last updated on…
Question Number 57010 by 121194 last updated on 28/Mar/19 $${f}\left(\frac{{x}+{y}}{\mathrm{2}}\right)=\frac{{f}\left({x}\right){f}\left({y}\right)}{{f}\left(\mathrm{2}\right)} \\ $$$${f}\left({x}\right)=? \\ $$ Commented by maxmathsup by imad last updated on 29/Mar/19 $${x}={y}\:\Rightarrow{f}\left({x}\right)=\frac{{f}^{\mathrm{2}} \left({x}\right)}{{f}\left(\mathrm{2}\right)}\:\:{with}\:{f}\left(\mathrm{2}\right)\neq\mathrm{0}\:\Rightarrow{f}^{\mathrm{2}}…
Question Number 57011 by 121194 last updated on 28/Mar/19 $${f}\left(\frac{{x}+{y}}{\mathrm{2}}\right){f}\left(\frac{{x}−{y}}{\mathrm{2}}\right)={g}\left({x}\right) \\ $$$${g}\left({x}+{y}\right){g}\left({x}−{y}\right)=\left[{f}\left({x}\right)\right]^{\mathrm{2}} −\left[{f}\left({y}\right)\right]^{\mathrm{2}} \\ $$$${f}\left({x}\right),{g}\left({x}\right)=? \\ $$ Answered by kaivan.ahmadi last updated on 28/Mar/19 $${g}\left({x}\right)…
Question Number 56962 by turbo msup by abdo last updated on 27/Mar/19 $${find}\:{S}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:{k}^{\mathrm{2}} \:{C}_{{n}} ^{{k}} \:{cos}\left(\mathrm{2}{kx}\right) \\ $$$${interms}\:{of}\:{n}. \\ $$ Commented by…