Question Number 140604 by ajfour last updated on 10/May/21 $${y}={x}^{\mathrm{3}} −{x}−{c}\:\:\:;\:{find}\:{the}\:{roots}. \\ $$$$\:\:\mathrm{0}\leqslant{c}\leqslant\frac{\mathrm{2}}{\mathrm{3}\sqrt{\mathrm{3}}} \\ $$ Answered by ajfour last updated on 11/May/21 Commented by ajfour…
Question Number 9533 by FilupSmith last updated on 14/Dec/16 $$\mathrm{Determine}\:\mathrm{and}\:\mathrm{prove}\:\mathrm{if}\:\mathrm{true}: \\ $$$$\int_{\mathrm{0}} ^{\:{n}} {x}^{\mathrm{2}} {dx}\:<\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{k}^{\mathrm{2}} \\ $$ Answered by geovane10math last updated on…
Question Number 140606 by mathsuji last updated on 10/May/21 $$\left(\mathrm{1}+{x}\right)^{\mathrm{2023}} \left(\mathrm{1}−{x}+{x}^{\mathrm{2}} \right)^{\mathrm{2022}} ={a}_{\mathrm{0}} +{a}_{\mathrm{1}} {x}+{a}_{\mathrm{2}} {x}^{\mathrm{2}} +…+{a}_{\mathrm{6067}} {x}^{\mathrm{6067}} \\ $$$${also}\:{if}\:{the}\:{equations} \\ $$$${a}_{{n}} \equiv\:\mathrm{1}\left({mod}\:\mathrm{5}\right)\:,\:{a}_{{n}} \equiv\:\mathrm{2}\left({mod}\:\mathrm{5}\right)\:,\:{n}=\mathrm{0};\mathrm{1};\mathrm{2};…;\mathrm{6067} \\…
Question Number 9532 by FilupSmith last updated on 14/Dec/16 $${S}=\underset{{n}={t}} {\overset{{k}} {\sum}}\left(\mathrm{2}{n}−\mathrm{1}\right) \\ $$$${S}=? \\ $$ Commented by sou1618 last updated on 14/Dec/16 $${S}=\left\{\underset{{n}=\mathrm{1}} {\overset{{k}}…
Question Number 140601 by mathdanisur last updated on 10/May/21 $$\underset{\mathrm{0}} {\overset{\infty} {\int}}\frac{{log}\left(\mathrm{1}+{z}^{\mathrm{4}} \right)}{\:\sqrt{{z}}\left(\mathrm{1}+{z}\right)}{dz} \\ $$ Answered by mathmax by abdo last updated on 10/May/21 $$\Phi=\int_{\mathrm{0}}…
Question Number 75066 by ~blr237~ last updated on 06/Dec/19 $$\mathrm{Prove}\:\:\mathrm{that}\:\mathrm{if}\:\:\mathrm{f}\:\mathrm{is}\:\mathrm{a}\:\mathrm{function}\:\mathbb{R}\rightarrow\mathbb{R}\: \\ $$$$\mathrm{and}\:\:\mathrm{there}\:\mathrm{exist}\:\mathrm{x}_{\mathrm{0}} >\mathrm{0}\:\:,\:\mathrm{such}\:\mathrm{as}\:\:\mathrm{L}\left(\mathrm{f}\right)\left(\mathrm{x}_{\mathrm{0}} \right)\:\mathrm{exist}\: \\ $$$$\mathrm{then}\:\underset{\mathrm{t}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{f}\left(\mathrm{t}\right)\mathrm{e}^{−\mathrm{x}_{\mathrm{0}} \mathrm{t}} =\mathrm{0}\:\mathrm{and}\:\forall\:\mathrm{x}>\mathrm{x}_{\mathrm{0}} \:\:\mathrm{L}\left(\mathrm{f}\right)\left(\mathrm{x}\right)\:\mathrm{exist}. \\ $$$$\mathrm{L}\left(\mathrm{f}\right)\:\mathrm{is}\:\mathrm{the}\:\mathrm{Laplace}\:\mathrm{transformed}\:\mathrm{function} \\ $$ Answered…
Question Number 9530 by geovane10math last updated on 12/Dec/16 $$\mathrm{Why}\:\:{i}\:\ngtr\:\mathrm{0}\:\mathrm{and}\:{i}\:\nless\:\mathrm{0}\:???? \\ $$ Commented by geovane10math last updated on 14/Dec/16 $${why} \\ $$ Answered by nume1114…
Question Number 140603 by BHOOPENDRA last updated on 10/May/21 Commented by BHOOPENDRA last updated on 10/May/21 $${mr}.{W}\:{sir}? \\ $$ Answered by mr W last updated…
Question Number 140597 by bramlexs22 last updated on 10/May/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{circle}\:\mathrm{which} \\ $$$$\mathrm{passes}\:\mathrm{through}\:\mathrm{the}\:\mathrm{point}\:\left(\mathrm{2},\mathrm{0}\right)\:\mathrm{and} \\ $$$$\mathrm{whose}\:\mathrm{center}\:\mathrm{is}\:\mathrm{the}\:\mathrm{limit}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{point}\:\mathrm{of}\:\mathrm{intersection}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{lines}\:\mathrm{3x}+\mathrm{5y}=\mathrm{1}\:\mathrm{and}\:\left(\mathrm{2}+\mathrm{c}\right)\mathrm{x}+\mathrm{5c}^{\mathrm{2}} \mathrm{y}=\mathrm{1} \\ $$$$\mathrm{as}\:\mathrm{c}\rightarrow\mathrm{1}\:. \\ $$ Answered by…
Question Number 9527 by Joel575 last updated on 12/Dec/16 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$${x}^{\mathrm{2}{n}} \:\geqslant\:\left({x}−\mathrm{1}\right)^{\mathrm{2}{n}} \:+\:\left(\mathrm{2}{x}−\mathrm{1}\right)^{{n}} \\ $$$${x}\:\geqslant\:\frac{\mathrm{1}}{\mathrm{2}},\:\:{n}\:\mathrm{is}\:\mathrm{positive}\:\mathrm{integers} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com