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Author: Tinku Tara

if-a-n-n-4-n-n-1-x-dx-1-x-5-then-1-a-n-is-convergent-or-divergent-2-lim-n-a-n-

Question Number 211421 by universe last updated on 08/Sep/24 $$\:\:\:\:\mathrm{if}\:\mathrm{a}_{\mathrm{n}} \:=\:\mathrm{n}^{\mathrm{4}} \int_{\mathrm{n}} ^{\mathrm{n}+\mathrm{1}} \:\frac{\mathrm{x}\:\mathrm{dx}}{\mathrm{1}+\mathrm{x}^{\mathrm{5}} }\:\:\mathrm{then} \\ $$$$\:\:\:\:\left(\mathrm{1}\right)\:\Sigma\mathrm{a}_{\mathrm{n}} \:\mathrm{is}\:\mathrm{convergent}\:\mathrm{or}\:\mathrm{divergent}?? \\ $$$$\:\:\:\:\left(\mathrm{2}\right)\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{a}_{\mathrm{n}\:} \:=\:?? \\ $$ Answered…

Question-211419

Question Number 211419 by maryaaaa last updated on 08/Sep/24 Answered by mahdipoor last updated on 08/Sep/24 $$\left.{salam}\:\::\right) \\ $$$${f}\left({x}\right)={x}^{\mathrm{2}} −\mathrm{2}\left[{x}\right]\:\:\:,\:\:\:{f}\left(−\frac{{f}\left(\sqrt{\mathrm{3}}\right)}{\mathrm{2}}\right)=? \\ $$$${f}\left(\sqrt{\mathrm{3}}\right)=\left(\sqrt{\mathrm{3}}\right)^{\mathrm{2}} −\mathrm{2}\left[\sqrt{\mathrm{3}}\right]=\mathrm{3}−\mathrm{2}×\mathrm{1}=\mathrm{1} \\ $$$${f}\left(−\frac{\mathrm{1}}{\mathrm{2}}\right)=\left(−\mathrm{0}.\mathrm{5}\right)^{\mathrm{2}}…

Question-211414

Question Number 211414 by AlagaIbile last updated on 08/Sep/24 Answered by Frix last updated on 08/Sep/24 $$\mathrm{Let}\:{x}_{{j}} \leqslant{x}_{{j}+\mathrm{1}} \\ $$$$\frac{\mathrm{1}}{{x}_{\mathrm{1}} }=\mathrm{1}\:\Rightarrow\:\mathrm{max}\:\left({x}_{\mathrm{1}} \right)\:=\mathrm{1} \\ $$$$\frac{\mathrm{1}}{{x}_{\mathrm{1}} }+\frac{\mathrm{1}}{{x}_{\mathrm{2}}…

Question-211402

Question Number 211402 by efronzo1 last updated on 08/Sep/24 Answered by A5T last updated on 08/Sep/24 $${Q}\mathrm{211029},\:{we}\:{can}\:{find}\:{a}\:{polynomial}\:{f}\left({x}\right) \\ $$$${f}\left({x}\right)={x}^{{n}} \underset{−} {+}\mathrm{1} \\ $$$${f}\left(\mathrm{3}\right)=\mathrm{28}\Rightarrow{f}\left({x}\right)={x}^{\mathrm{3}} +\mathrm{1} \\…