Question Number 186021 by Spillover last updated on 30/Jan/23 $${prove}\:{that}\left({using}\:{Epsilon}−{Delta}\:{definition}\right) \\ $$$$\left({a}\right)\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\left(\mathrm{6}{x}−\mathrm{2}\right)=\mathrm{4} \\ $$$$\left({b}\right)\underset{{x}\rightarrow\mathrm{6}} {\mathrm{lim}}\sqrt{\mathrm{3}{x}−\mathrm{2}}=\mathrm{4} \\ $$ Answered by aba last updated on 30/Jan/23…
Question Number 54948 by tarun kunar last updated on 15/Feb/19 $$\alpha,\beta\:{are}\:{the}\:{roots}\:{and}\:{prove}\:{that}\:\alpha^{{n}} +\beta^{{n}} =\mathrm{2}\left[\mathrm{cos}\:{n}\Pi/\mathrm{2}\right] \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 15/Feb/19 $${write}\:{the}\:{eqn}… \\ $$…
Question Number 186022 by Spillover last updated on 30/Jan/23 $${prove}\:\:{that}\left({using}\:{Epsilon}−{Delta}\:{definition}\right) \\ $$$$\left({a}\right)\:\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\left(\:\mathrm{2}{x}^{\mathrm{2}} +\mathrm{1}\right)=\mathrm{19} \\ $$$$\left({b}\right)\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:{x}^{\mathrm{3}} =\mathrm{8} \\ $$ Commented by mr W last…
Question Number 120480 by mathocean1 last updated on 31/Oct/20 $${show}\:{that}\:\forall\:{n}\:\in\mathbb{N}^{\ast} \\ $$$$\sum_{{k}=\mathrm{1}} ^{{n}} {k}\left({n}−{k}\right)=\frac{\left({n}−\mathrm{1}\right)\left({n}+\mathrm{1}\right)}{\mathrm{6}} \\ $$ Answered by Ar Brandon last updated on 31/Oct/20 $$\mathrm{S}_{\mathrm{k}}…
Question Number 120475 by Jamshidbek2311 last updated on 31/Oct/20 Answered by mathmax by abdo last updated on 31/Oct/20 $$\mathrm{if}\:\mathrm{we}\:\mathrm{consider}\:\mathrm{congruence}\:\mathrm{modulo}\:\mathrm{2}\:\mathrm{e}\Rightarrow\overset{−^{\mathrm{2}} } {\mathrm{x}}+\overset{−} {\mathrm{x}}=\overset{−} {\mathrm{0}}\:\Rightarrow \\ $$$$\overset{−}…
Question Number 120472 by mathocean1 last updated on 31/Oct/20 $${A}=\overline {\mathrm{5}{x}\mathrm{23}}\:^{\mathrm{6}} \:{show}\:{that}\:{A}\equiv{x}−\mathrm{4}\left[\mathrm{7}\right] \\ $$$${deduct}\:{the}\:{value}\:{of}\:{x}\:{for}\:{which}\:{A}\:{is}\: \\ $$$${divisible}\:{by}\:\mathrm{7} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 120470 by mathocean1 last updated on 31/Oct/20 $${solve}\:{in}\:{function}\:{of}\:{n}: \\ $$$$\mathrm{2}^{{n}} \equiv{x}−\mathrm{4}\left[\mathrm{3}\right] \\ $$$${n}\in\mathbb{N} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 120471 by mathocean1 last updated on 31/Oct/20 $${solve}\:{in}\:\mathbb{Z}\:{x}^{\mathrm{3}} +\mathrm{2}{x}+\mathrm{1}\equiv\mathrm{1}\left[\mathrm{4}\right] \\ $$ Answered by Ar Brandon last updated on 31/Oct/20 $$\mathrm{x}^{\mathrm{3}} +\mathrm{2x}+\mathrm{1}=\mathrm{1}\left[\mathrm{4}\right]\Rightarrow\mathrm{x}^{\mathrm{3}} +\mathrm{2x}=\mathrm{0}\left[\mathrm{4}\right] \\…
Question Number 120469 by mathocean1 last updated on 31/Oct/20 $${c}\:{alculate}\:{the}\:{rest}\:{of}\:{the}\:{division}\:{of} \\ $$$$\mathrm{2}^{{n}} \:{by}\:\mathrm{3}\:;\:{n}\:\in\:\mathbb{N} \\ $$ Answered by mathmax by abdo last updated on 31/Oct/20 $$\mathrm{n}=\mathrm{2k}\:\Rightarrow\mathrm{2}^{\mathrm{n}}…
Question Number 120464 by pooooop last updated on 31/Oct/20 Answered by Jamshidbek2311 last updated on 31/Oct/20 $$\sqrt{{x}−\mathrm{1}}={a}\:\:\Rightarrow\:{x}={a}^{\mathrm{2}} +\mathrm{1} \\ $$$$\sqrt{{y}−\mathrm{4}}={b}\:\Rightarrow\:{y}={b}^{\mathrm{2}} +\mathrm{4} \\ $$$$\sqrt{{z}−\mathrm{9}}={c}\:\Rightarrow\:{z}={c}^{\mathrm{2}} +\mathrm{9}\: \\…