Question Number 120545 by pooooop last updated on 01/Nov/20 $$\left(\sqrt{\boldsymbol{{x}}}\right)^{\frac{\boldsymbol{{x}}}{\:\sqrt{\boldsymbol{{x}}}}} \:=\:\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:\:\:\:\:\boldsymbol{{x}}=? \\ $$ Commented by pooooop last updated on 01/Nov/20 $$ \\ $$$$\:\:\:\left(\sqrt{{x}}\right)^{\frac{{x}\sqrt{{x}}}{{x}}} =\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \\…
Question Number 120529 by bemath last updated on 01/Nov/20 Commented by bemath last updated on 01/Nov/20 Answered by Dwaipayan Shikari last updated on 01/Nov/20 $$\:\:\:\:\:\:\:{S}=\mathrm{1}+\mathrm{2}{a}+\mathrm{3}{a}^{\mathrm{2}}…
Question Number 186053 by Rupesh123 last updated on 31/Jan/23 Answered by SEKRET last updated on 31/Jan/23 $$\:\:\boldsymbol{\mathrm{a}}^{\mathrm{2}} −\mathrm{5}\boldsymbol{\mathrm{a}}−\mathrm{1}=\mathrm{0}\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{a}}^{\mathrm{2}} =\mathrm{5}\boldsymbol{\mathrm{a}}+\mathrm{1} \\ $$$$\:\:\:\:\:\boldsymbol{\mathrm{a}}^{\mathrm{3}} =\mathrm{5}\boldsymbol{\mathrm{a}}^{\mathrm{2}} +\boldsymbol{\mathrm{a}}=\mathrm{5}\left(\mathrm{5}\boldsymbol{\mathrm{a}}+\mathrm{1}\right)+\boldsymbol{\mathrm{a}}=\mathrm{26}\boldsymbol{\mathrm{a}}+\mathrm{5} \\ $$$$\:\:\:\left(\mathrm{26}\boldsymbol{\mathrm{a}}+\mathrm{5}\right)^{\mathrm{2}}…
Question Number 54983 by ajfour last updated on 15/Feb/19 $${Find}\:{shortest}\:{distance}\:{from}\:{origin} \\ $$$${to}\:{the}\:{cubic}\:\:\:{y}={x}^{\mathrm{3}} −\mathrm{10}{x}^{\mathrm{2}} +\mathrm{27}{x}−\mathrm{18}. \\ $$ Commented by mr W last updated on 15/Feb/19 $${you}\:{can}\:{apply}\:{your}\:{solution}\:{method}\:{for}…
Question Number 186025 by SAMIRA last updated on 31/Jan/23 $$\boldsymbol{\mathrm{P}}\left(\boldsymbol{{x}}\right)\:=\:−\mathrm{3}\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{5}\boldsymbol{\mathrm{x}}^{\mathrm{3}} +\mathrm{5}\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{5}\boldsymbol{\mathrm{x}}−\mathrm{2} \\ $$$${division}\:{euclidienne}\:{par}\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{1} \\ $$$$ \\ $$ Commented by Rasheed.Sindhi last updated…
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{−}…