Question Number 163719 by HongKing last updated on 09/Jan/22 $$\mathrm{Evaluate}\:\mathrm{the}\:\mathrm{following}\:\mathrm{limit}: \\ $$$$\Phi\:=\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:-\:\frac{\mathrm{1}}{\mathrm{n}!}\:\centerdot\:\frac{\mathrm{d}^{\boldsymbol{\mathrm{n}}} }{\mathrm{dx}^{\boldsymbol{\mathrm{n}}} }\:\left(\frac{\mathrm{e}^{\boldsymbol{\mathrm{x}}-\mathrm{1}} }{\mathrm{x}\:-\:\mathrm{1}}\right)\mid_{\boldsymbol{\mathrm{x}}=\mathrm{0}} \\ $$ Answered by Mathspace last updated on 09/Jan/22…
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Question Number 32632 by Tinkutara last updated on 29/Mar/18 Commented by mrW2 last updated on 30/Mar/18 $$\left(\mathrm{1}+{x}^{\mathrm{12}} +{x}^{\mathrm{24}} +{x}^{\mathrm{36}} \right)\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{12}} \\ $$$${C}_{\mathrm{10}} ^{\mathrm{12}} +{C}_{\mathrm{4}}…
Question Number 32629 by rahul 19 last updated on 29/Mar/18 $$\boldsymbol{{I}}{f}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{9}\:,\:\mathrm{4}{a}^{\mathrm{2}} +\mathrm{9}{b}^{\mathrm{2}} =\mathrm{16}, \\ $$$${then}\:\boldsymbol{{maximum}}\:{value}\:{of}\: \\ $$$$\mathrm{4}{a}^{\mathrm{2}} {x}^{\mathrm{2}} +\mathrm{9}{b}^{\mathrm{2}} {y}^{\mathrm{2}} −\mathrm{12}{abxy}\:{is}\:? \\ $$…
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Question Number 32584 by Tinkutara last updated on 28/Mar/18 Answered by Joel578 last updated on 28/Mar/18 $$\mathrm{10}! \\ $$ Commented by Tinkutara last updated on…
Question Number 163651 by mathlove last updated on 09/Jan/22 $${if}\:\:\left({a}−\mathrm{2}{b}\right)^{\mathrm{2}} +\left({b}−\mathrm{2}{c}\right)^{\mathrm{2}} =\mathrm{0} \\ $$$${find}\:\:{volve}\:\:\frac{\left({b}+{c}−{a}\right)^{\mathrm{3}} }{{abc}}=? \\ $$ Commented by cortano1 last updated on 09/Jan/22 $$\left.\begin{matrix}{{a}=\mathrm{2}{b}\Rightarrow{b}=\frac{\mathrm{1}}{\mathrm{2}}{a}}\\{{b}=\mathrm{2}{c}\Rightarrow{c}=\frac{\mathrm{1}}{\mathrm{4}}{a}}\end{matrix}\right\}\:\Rightarrow\frac{−\frac{\mathrm{1}}{\mathrm{64}}{a}^{\mathrm{3}}…
Question Number 32563 by rahul 19 last updated on 27/Mar/18 $$\boldsymbol{{T}}{he}\:{set}\:{of}\:{values}\:{of}\:'{a}'\:{for}\:{which}\: \\ $$$${all}\:{the}\:{solutions}\:{of}\:{the}\:{equation} \\ $$$$\mathrm{4sin}\:^{\mathrm{4}} {x}+{a}\mathrm{sin}\:^{\mathrm{2}} {x}+\mathrm{3}=\mathrm{0}\:{are}\:{real}\:{and}\: \\ $$$${distinct}\:{is}\:? \\ $$ Commented by rahul 19…
Question Number 163632 by HongKing last updated on 08/Jan/22 $$\frac{\left(\mathrm{x}^{\mathrm{2}} \:-\:\mathrm{y}^{\mathrm{2}} \right)\centerdot\sqrt{\mathrm{3}}}{\:\sqrt{\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{3x}^{\mathrm{2}} \mathrm{y}\:+\:\mathrm{3xy}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{3}} }}\:=\:-\mathrm{1} \\ $$$$\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{3}} \:=\:\left(\mathrm{x}\:+\:\mathrm{y}\right)^{\mathrm{2}} \\ $$$$\mathrm{find}:\:\:\boldsymbol{\mathrm{x}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{y}} \\ $$ Answered…
Question Number 163624 by amin96 last updated on 08/Jan/22 Answered by mr W last updated on 09/Jan/22 $${A}=\mathrm{2}^{\mathrm{21}} ×\mathrm{17}^{\mathrm{24}} \\ $$$${full}\:{squares}: \\ $$$$\mathrm{1}\:\Rightarrow\:\mathrm{1} \\ $$$$\mathrm{2}^{\mathrm{2}}…