Question Number 119815 by bemath last updated on 27/Oct/20 $${Given}\:{f}\left({x}+{y}\right)=\mathrm{4}{f}\left({x}\right).{f}\left({y}\right)\:{for} \\ $$$${all}\:{real}\:{numbers}\:{x}\:{and}\:{y}. \\ $$$${If}\:{f}\left(\mathrm{3}\right)=\mathrm{32}\:{then}\:{f}\left(\mathrm{1}\right)=\_ \\ $$ Answered by Olaf last updated on 27/Oct/20 $${f}\left(\mathrm{1}+\mathrm{1}\right)\:=\:\mathrm{4}{f}\left(\mathrm{1}\right){f}\left(\mathrm{1}\right) \\…
Question Number 119754 by Bird last updated on 26/Oct/20 $${find}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{{u}_{{n}} }{{n}!}\:{if}\:\:{u}_{{n}} \:={u}_{{n}+\mathrm{1}} +{u}_{{n}−\mathrm{1}} \\ $$ Commented by Dwaipayan Shikari last updated on 26/Oct/20…
Question Number 185211 by Rupesh123 last updated on 18/Jan/23 Answered by manolex last updated on 18/Jan/23 $${x} \\ $$$$ \\ $$ Answered by manolex last…
Question Number 53961 by maxmathsup by imad last updated on 27/Jan/19 $${let}\:\varphi\left({x}\right)\:=\frac{{arctan}\left(\mathrm{2}{x}\right)}{\mathrm{1}−{x}^{\mathrm{2}} } \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\varphi^{\left({n}\right)} \left({x}\right)\: \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\varphi^{\left({n}\right)} \left(\mathrm{0}\right)\:{anddevelpp}\:\varphi\:{at}\:{integr}\:{serie} \\ $$ Commented by maxmathsup by…
Question Number 53960 by maxmathsup by imad last updated on 27/Jan/19 $${let}\:{f}\left({x}\right)\:={arctan}\left({x}^{\mathrm{2}} \right)\:{developp}\:{f}\:{at}\:{i}\:{serie}. \\ $$$${the}\:{Q}\:.\:{is}\:{developp}\:{f}\:{at}\:{integr}\:{serie}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 53957 by maxmathsup by imad last updated on 05/Feb/19 $${let}\:{f}\left({x}\right)\:={arctan}\left(\mathrm{1}+\mathrm{2}{x}\right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right)\:{then}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}\:. \\ $$$${we}\:{have}\:{f}^{'} \left({x}\right)=\frac{\mathrm{2}}{\mathrm{1}+\left(\mathrm{1}+\mathrm{2}{x}\right)^{\mathrm{2}} }\:\Rightarrow\:{f}^{\left({n}\right)} \left({x}\right)\:=\mathrm{2}\:\left\{\frac{\mathrm{1}}{\left(\mathrm{2}{x}+\mathrm{1}\right)^{\mathrm{2}} +\mathrm{1}}\right\}^{\left({n}−\mathrm{1}\right)} \:\:{with}\:{n}>\mathrm{0}…
Question Number 53947 by maxmathsup by imad last updated on 27/Jan/19 $${let}\:{U}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{\mathrm{1}}{{k}\left[\sqrt{{k}}\right]} \\ $$$${find}\:{a}\:{equivalent}\:{of}\:{U}_{{n}} \:{when}\:{n}\rightarrow+\infty \\ $$ Terms of Service Privacy Policy…
Question Number 119391 by Don08q last updated on 24/Oct/20 $$\:\mathrm{Given}\:\mathrm{that}\:{f}\left({x}−\mathrm{3}\right)\:=\:{x}^{\mathrm{2}} \:−\:\mathrm{12}{x}\:+\:\mathrm{41} \\ $$$$\:\mathrm{find}\:\mathrm{an}\:\mathrm{explicit}\:\mathrm{expression}\:\mathrm{for}\:{f}\left({x}\right) \\ $$$$ \\ $$$$\:{please}\:{I}\:\:{need}\:{the}\:{procedure} \\ $$ Answered by bemath last updated on…
Question Number 53795 by maxmathsup by imad last updated on 25/Jan/19 $${calculate}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{4}{n}+\mathrm{1}}\:=\mathrm{1}−\frac{\mathrm{1}}{\mathrm{5}}\:+\frac{\mathrm{1}}{\mathrm{9}}\:−\frac{\mathrm{1}}{\mathrm{13}}\:+…. \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 53781 by maxmathsup by imad last updated on 25/Jan/19 $${calculateA}_{{n}} =\sum_{{n}=\mathrm{1}} ^{\infty} \:{x}^{{n}} {cos}\left({n}\theta\right)\:\:{and}\:{B}_{{n}} =\sum_{{n}=\mathrm{1}} ^{\infty} \:{x}^{{n}} {sin}\left({n}\theta\right) \\ $$ Commented by maxmathsup…