Question Number 125264 by mohammad17 last updated on 09/Dec/20 Answered by Ar Brandon last updated on 09/Dec/20 $$\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}=\mathrm{0}\:\Rightarrow\:\mathrm{x}^{\mathrm{2}} =\mathrm{x}−\mathrm{1} \\ $$$$\Rightarrow\mathrm{x}^{\mathrm{3}} =\mathrm{x}^{\mathrm{2}} −\mathrm{x}=\mathrm{x}−\mathrm{1}−\mathrm{x}=−\mathrm{1} \\…
Question Number 59727 by muneshkumar last updated on 14/May/19 $${a}={b}^{\mathrm{2}{p}\:\:} {b}={c}^{\mathrm{2}{q}\:} \:{c}={a}^{\mathrm{2}{r}} \:{prove}\:{that}\:{pqr}=\frac{\mathrm{1}}{\mathrm{8}} \\ $$ Answered by MJS last updated on 13/May/19 $$\mathrm{ln}\:{a}\:=\mathrm{2}{p}\mathrm{ln}\:{b} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{ln}\:{b}\:=\mathrm{2}{q}\mathrm{ln}\:{c}…
Question Number 125263 by mohammad17 last updated on 09/Dec/20 Commented by mohammad17 last updated on 09/Dec/20 $${help}\:{me}\:{sir} \\ $$ Answered by Olaf last updated on…
Question Number 125256 by 676597498 last updated on 09/Dec/20 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{6}^{{n}} }{\left(\mathrm{3}^{{n}} −\mathrm{2}^{{n}} \right)\left(\mathrm{3}^{{n}+\mathrm{1}} −\mathrm{2}^{{n}+\mathrm{1}} \right)} \\ $$ Answered by mathmax by abdo last…
Question Number 125257 by Schwartzman94 last updated on 09/Dec/20 $${S}=\frac{{C}_{{n}} ^{\mathrm{0}} }{{C}_{{n}+\mathrm{2}} ^{\mathrm{1}} }+\frac{{C}_{{n}} ^{\mathrm{1}} }{{C}_{{n}+\mathrm{2}} ^{\mathrm{2}} }+…+\frac{{C}_{{n}} ^{{n}} }{{C}_{{n}+\mathrm{2}} ^{{n}+\mathrm{1}} } \\ $$ Commented…
Question Number 190781 by Tawa11 last updated on 11/Apr/23 Commented by mr W last updated on 11/Apr/23 $${if}\:{you}\:{understand}\:{the}\:{question},\:{then} \\ $$$${you}\:{should}\:{be}\:{able}\:{to}\:{solve}\:{it}.\:{i}\:{don}'{t} \\ $$$${understand}\:{the}\:{question},\:{so}\:{i}\:{can}'{t} \\ $$$${solve}\:{it}.\:{i}\:{don}'{t}\:{understand}\:{it},\:{because} \\…
Question Number 125249 by mohammad17 last updated on 09/Dec/20 Answered by Dwaipayan Shikari last updated on 09/Dec/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−\left(\mathrm{1}+\frac{{x}}{\mathrm{2}}\right)\left(\mathrm{1}−\frac{{x}}{\mathrm{3}}\right)\left(\mathrm{1}+\frac{{x}}{\mathrm{4}}\right)\left(\mathrm{1}−\frac{{x}}{\mathrm{5}}\right)…\left(\mathrm{1}+\frac{{x}}{\mathrm{2}{n}}\right)\left(\mathrm{1}−\frac{{x}}{\mathrm{2}{n}+\mathrm{1}}\right)}{{x}} \\ $$$$=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−\underset{{n}=\mathrm{1}} {\overset{{n}} {\prod}}\left(\mathrm{1}+\frac{{x}}{\mathrm{2}{n}}\right)\underset{{n}=\mathrm{1}} {\overset{{n}}…
Question Number 125247 by amns last updated on 09/Dec/20 $${Is}\:{cos}\mathrm{2}\pi\:=\:\mathrm{1}\:\:??? \\ $$ Commented by john_santu last updated on 09/Dec/20 $${is}\:\mathrm{sin}\:\frac{\pi}{\mathrm{2}}\:=\:\mathrm{1}?\: \\ $$ Answered by MJS_new…
Question Number 125240 by hatakekakashi1729gmailcom last updated on 09/Dec/20 Commented by Dwaipayan Shikari last updated on 09/Dec/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} {xlog}\left({x}\right)\:{dx}\:\:\:\:\:{logx}={t}\Rightarrow\frac{\mathrm{1}}{{x}}=\frac{{dt}}{{dx}} \\ $$$$=\int_{−\infty} ^{\mathrm{0}} {te}^{\mathrm{2}{t}} \:\:\:{dt}\:\:\:\:\:\mathrm{2}{t}=−{u}…
Question Number 190779 by 07049753053 last updated on 11/Apr/23 $$\boldsymbol{\mathrm{R}{e}}\left(\frac{\mathrm{1}}{\mathrm{1}−\boldsymbol{{a}}}\right)^{\boldsymbol{{a}}−\mathrm{1}} \\ $$ Answered by Frix last updated on 11/Apr/23 $${f}\left({a}\right)=\left(\frac{\mathrm{1}}{\mathrm{1}−{a}}\right)^{{a}−\mathrm{1}} \in\mathbb{R}\forall{a}<\mathrm{1} \\ $$$$\underset{{a}\rightarrow\mathrm{1}} {\mathrm{lim}}\:{f}\left({a}\right)\:=\mathrm{1} \\…