Question Number 205151 by mathzup last updated on 10/Mar/24 $${find}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{ln}^{\mathrm{2}} {x}}{\mathrm{1}+{x}^{\mathrm{4}} }{dx} \\ $$ Answered by Berbere last updated on 12/Mar/24 $$\Omega=\int_{−\infty} ^{\mathrm{0}}…
Question Number 205147 by Ghisom last updated on 10/Mar/24 $$\mathrm{solve}\:\mathrm{for}\:{z}\in\mathbb{C} \\ $$$${z}\mathrm{ln}\:{z}\:={z}−\mathrm{2} \\ $$ Answered by pi314 last updated on 10/Mar/24 $${z}={e}^{{y}} \\ $$$$\Leftrightarrow{ye}^{{y}} ={e}^{{y}}…
Question Number 205156 by depressiveshrek last updated on 11/Mar/24 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{determinant}: \\ $$$$\begin{vmatrix}{\mathrm{5}}&{\mathrm{3}}&{\mathrm{0}}&{\mathrm{0}}&{\ldots}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{2}}&{\mathrm{5}}&{\mathrm{3}}&{\mathrm{0}}&{\ldots}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{2}}&{\mathrm{5}}&{\mathrm{3}}&{\ldots}&{\mathrm{0}}&{\mathrm{0}}\\{\vdots}&{\vdots}&{\vdots}&{\vdots}&{\ddots}&{\vdots}&{\vdots}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\ldots}&{\mathrm{5}}&{\mathrm{3}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\ldots}&{\mathrm{2}}&{\mathrm{5}}\end{vmatrix} \\ $$ Answered by pi314 last updated on 11/Mar/24 $$\Delta_{{n}} =\begin{vmatrix}{\mathrm{5}\:\mathrm{3}\:\:\:\mathrm{0}\:\mathrm{0}……\mathrm{0}\:\mathrm{0}}\\{\mathrm{2}\:\:\mathrm{5}\:\:\mathrm{3}\:\mathrm{0}……\mathrm{0}\:\mathrm{0}}\\{\mathrm{0}\:\:\mathrm{2}\:\:\mathrm{5}\:\mathrm{3}……\mathrm{0}\:\:\mathrm{0}}\\{………………\mathrm{5}\:\mathrm{3}}\\{\mathrm{0}\:\mathrm{0}\:\mathrm{0}\:\:\mathrm{0}…….\:\mathrm{2}\:\mathrm{5}}\end{vmatrix} \\ $$$$\Delta_{{n}}…
Question Number 205141 by Tinku Tara last updated on 10/Mar/24 $$\mathrm{Server}\:\mathrm{is}\:\mathrm{back}\:\mathrm{up}\:\mathrm{and}\:\mathrm{running}. \\ $$$$\mathrm{Post}\:\mathrm{a}\:\mathrm{message}\:\mathrm{if}\:\mathrm{you}\:\mathrm{face}\:\mathrm{any}\:\mathrm{issues}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 205142 by universe last updated on 10/Mar/24 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{n}^{−\mathrm{n}^{\mathrm{2}} } \left[\left(\mathrm{n}+\mathrm{1}\right)\left(\mathrm{n}+\frac{\mathrm{1}}{\mathrm{2}}\right)\left(\mathrm{n}+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }\right)…\left(\mathrm{n}+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{n}−\mathrm{1}} }\right)\right]^{\mathrm{n}} =? \\ $$ Answered by pi314 last updated on 10/Mar/24…
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Question Number 205138 by Thokna last updated on 10/Mar/24 $${A}=\underset{{x}\rightarrow\mathrm{0}\:\:} {\mathrm{lim}}\frac{\mathrm{1}−\mathrm{cos2}{x}}{\mathrm{2}{x}^{\mathrm{2}} } \\ $$$$\:\:\:\:=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{2sin}^{\mathrm{2}} {x}}{\mathrm{2}{x}^{\mathrm{2}} } \\ $$$$\:\:\:\:=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{sin}{x}}{{x}}\right)^{\mathrm{2}} =\mathrm{1} \\ $$$${B}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}}{{x}\mathrm{cot}{x}} \\…
Question Number 205155 by depressiveshrek last updated on 10/Mar/24 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{determinant}: \\ $$$$\begin{vmatrix}{\mathrm{1}−\lambda}&{\mathrm{1}}&{\mathrm{1}}&{\ldots}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{1}−\lambda}&{\mathrm{1}}&{\ldots}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}−\lambda}&{\ldots}&{\mathrm{1}}\\{\vdots}&{\vdots}&{\vdots}&{\ddots}&{\vdots}\\{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\ldots}&{\mathrm{1}−\lambda}\end{vmatrix} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 205116 by universe last updated on 09/Mar/24 $$\:\:\mathrm{let}\:\mathrm{x}^{\mathrm{2}} −\mathrm{3x}+\mathrm{p}\:=\:\mathrm{0}\:\mathrm{has}\:\mathrm{two}\:\mathrm{positive}\:\mathrm{roots} \\ $$$$\:'\mathrm{a}'\:\mathrm{and}\:'\mathrm{b}'\:\mathrm{then}\:\:\mathrm{inf}\left(\frac{\mathrm{4}}{\mathrm{a}}+\frac{\mathrm{1}}{\mathrm{b}}\right)\:\mathrm{is}\: \\ $$ Answered by pi314 last updated on 09/Mar/24 $$\frac{\mathrm{4}{b}+{a}}{{ab}}=\frac{\mathrm{3}+\mathrm{3}{b}}{{p}} \\ $$$$\mathrm{9}−\mathrm{4}{p}\geqslant\mathrm{0};{p}\leqslant\frac{\mathrm{9}}{\mathrm{4}}…
Question Number 205117 by BaliramKumar last updated on 09/Mar/24 Answered by Rasheed.Sindhi last updated on 09/Mar/24 $$\frac{{x}}{{y}}+\frac{{y}}{{x}}=\mathrm{2} \\ $$$$\Rightarrow{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{2}{xy} \\ $$$$\Rightarrow{x}^{\mathrm{2}} −\mathrm{2}{xy}+{y}^{\mathrm{2}} =\mathrm{0}…