Question Number 119250 by Pengu last updated on 23/Oct/20 Commented by Pengu last updated on 23/Oct/20 $$\mathrm{I}\:\mathrm{know}\:{a}_{{n}} ={a}_{{n}} ^{{h}} +{a}_{{n}} ^{{p}} \\ $$$${a}_{{n}} ^{{h}} \Rightarrow{a}_{{n}}…
Question Number 119214 by abdul88 last updated on 23/Oct/20 $${f}\left({x}\right)\:=\:\left(\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{f}\left({x}\right){dx}\right){x}^{\mathrm{2}} \:+\:\left(\underset{\mathrm{0}} {\overset{\mathrm{2}} {\int}}{f}\left({x}\right){dx}\right){x}\:+\:\left(\underset{\mathrm{0}} {\overset{\mathrm{3}} {\int}}{f}\left({x}\right){dx}\right)+\mathrm{1} \\ $$$${the}\:{valeu}\:{f}\left(\mathrm{4}\right)\:=\:? \\ $$ Answered by bemath last…
Question Number 53466 by maxmathsup by imad last updated on 22/Jan/19 $${let}\:{U}_{{n}} =\frac{\mathrm{1}}{{n}}\left\{\prod_{{k}=\mathrm{1}} ^{{n}} \left({n}+{k}\right)\right\}^{\frac{\mathrm{1}}{{n}}} \\ $$$${find}\:{lim}_{{n}\rightarrow+\infty} \:{U}_{{n}} \\ $$ Answered by Prithwish sen last…
Question Number 118960 by bramlexs22 last updated on 21/Oct/20 $$\:{Given}\:{f}:\:{R}\rightarrow{R}\:{and}\:{g}:\:{R}\rightarrow{R} \\ $$$${where}\:{f}\left({x}\right)={x}^{\mathrm{3}} +\mathrm{3}\:{and}\:{g}\left({x}\right)=\mathrm{2}{x}+\mathrm{1}.\:{Find} \\ $$$${the}\:{value}\:{of}\:{f}^{−\mathrm{1}} \left({g}^{−\mathrm{1}} \left(\mathrm{23}\right)\right). \\ $$ Answered by benjo_mathlover last updated on…
Question Number 118381 by bramlexs22 last updated on 17/Oct/20 $${How}\:{do}\:{you}\:{express}\:{this}\:{question} \\ $$$${in}\:{partial}\:{fraction}\:\frac{\mathrm{5}{x}^{\mathrm{2}} +{x}+\mathrm{6}}{\left(\mathrm{3}−\mathrm{2}{x}\right)\left({x}^{\mathrm{2}} +\mathrm{4}\right)}\: \\ $$$${hence}\:{obtain}\:{the}\:{expansion} \\ $$$${is}\:{ascending}\:{powers}\:{of}\:{x}\:{up} \\ $$$${to}\:{and}\:{including}\:{the}\:{term}\:{x}^{\mathrm{2}} \\ $$ Commented by bramlexs22…
Question Number 52682 by maxmathsup by imad last updated on 11/Jan/19 $${find}\:{nature}\:{of}\:{the}\:{serie}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\sqrt{{n}+\mathrm{1}}−\sqrt{{n}}}{{nln}\left({n}+\mathrm{1}\right)} \\ $$ Commented by Abdo msup. last updated on 12/Jan/19 $${let}\:{u}_{{n}}…
Question Number 52679 by maxmathsup by imad last updated on 11/Jan/19 $${let}\:{f}_{{n}} \left({x}\right)=\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}+{x}}\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{study}\:{the}\:{simple}\:{convergence}\:{of}\:\Sigma\:{f}_{{n}} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{f}^{'} \left({x}\right) \\ $$ Commented by maxmathsup…
Question Number 52677 by maxmathsup by imad last updated on 11/Jan/19 $${find}\:{nature}\:{of}\:\sum_{{n}=\mathrm{2}} ^{\infty} \left(−\mathrm{1}\right)^{{n}} \sqrt{{n}}{ln}\left(\frac{{n}+\mathrm{1}}{{n}−\mathrm{1}}\right). \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 52678 by maxmathsup by imad last updated on 11/Jan/19 $${let}\:{u}_{{n}} ={ln}\left\{{cos}\left(\mathrm{2}^{−{n}} \right)\right\}\:\:{calculate}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{u}_{{n}} \\ $$ Commented by Abdo msup. last updated on…
Question Number 52675 by maxmathsup by imad last updated on 11/Jan/19 $${let}\:{u}_{{n}} =\left(−\mathrm{1}\right)^{{n}} \int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{sin}^{{n}} {xdx}\:\:{calculate}\:\Sigma\:{u}_{{n}} \\ $$ Commented by maxmathsup by imad last…