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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} \\ $$$$\Rightarrow{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{2}{xy} \\ $$$$\Rightarrow{x}^{\mathrm{2}} −\mathrm{2}{xy}+{y}^{\mathrm{2}} =\mathrm{0}…
Question Number 205134 by universe last updated on 09/Mar/24 Answered by pi314 last updated on 09/Mar/24 $${nx}={y} \\ $$$$\Leftrightarrow{A}=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\int_{\mathrm{0}} ^{{n}} \frac{{f}\left(\frac{{y}}{{n}}\right)}{\left(\mathrm{1}+{y}^{\mathrm{2}} \right)}{dy}=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\int_{\mathrm{0}} ^{{n}}…
Question Number 205135 by mr W last updated on 09/Mar/24 Commented by mr W last updated on 09/Mar/24 $${ABCD}\:{is}\:{square}. \\ $$$${find}\:\frac{{red}\:{area}}{{blue}\:{area}}=? \\ $$ Answered by…
Question Number 205130 by Ari last updated on 09/Mar/24 Commented by Ari last updated on 09/Mar/24 $${x}=? \\ $$ Answered by A5T last updated on…
Question Number 205114 by 2kdw last updated on 09/Mar/24 $${Solve}: \\ $$$$ \\ $$$$\:\:{lim}_{\left({x},{y}\right)\rightarrow\left(\mathrm{0},\mathrm{0}\right)} \frac{\mathrm{1}−{cos}\left(\sqrt{\mathrm{10}{xy}}\right)}{\mathrm{3}.{y}.{sin}\left(\mathrm{22}{x}\right)} \\ $$$$ \\ $$$${Ans}.:\:\frac{\mathrm{5}}{\mathrm{66}} \\ $$$${Step}\:{by}\:{step},\:{please}! \\ $$ Answered by…
Question Number 205101 by universe last updated on 08/Mar/24 $$\:\:\mathrm{given}\:\mathrm{that}\:\mathrm{there}\:\mathrm{are}\:\mathrm{real}\:\mathrm{constant}\:\mathrm{a},\mathrm{b},\:\mathrm{c},\:\mathrm{d} \\ $$$$\:\:\mathrm{such}\:\mathrm{the}\:\mathrm{identity} \\ $$$$\:\lambda\mathrm{x}^{\mathrm{2}} +\mathrm{2xy}+\mathrm{y}^{\mathrm{2}} =\:\left(\mathrm{ax}+\mathrm{by}\right)^{\mathrm{2}} +\left(\mathrm{cx}+\mathrm{dy}\right)^{\mathrm{2}} \:\mathrm{holds} \\ $$$$\:\mathrm{for}\:\mathrm{all}\:\mathrm{x},\mathrm{y}\:\in\:\mathbb{R}\:\mathrm{this}\:\mathrm{implies} \\ $$$$\left({a}\right)\:\lambda=−\mathrm{5}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left({b}\right)\:\lambda\geqslant\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\left({c}\right)\mathrm{0}<\lambda<\mathrm{1} \\ $$$$\:\left({d}\right)\:\mathrm{there}\:\mathrm{is}\:\mathrm{no}\:\mathrm{such}\:\lambda\in\mathbb{R} \\…