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Question Number 189266 Answers: 1 Comments: 0
$$\:\:\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:\frac{\sqrt[{\mathrm{3}}]{\mathrm{tan}\:\mathrm{x}}}{\mathrm{1}+\mathrm{sin}\:\mathrm{2x}}\:\mathrm{dx}\:=? \\ $$
Question Number 189263 Answers: 0 Comments: 1
$$\boldsymbol{{evaluate}}\:\int\int_{\boldsymbol{\mathrm{E}}} \int\mathrm{15}{Zdv},\:{where}\:{E} \\ $$$$\:{is}\:{the}\:{region}\:{between}\:\mathrm{2}{x}+{y}+{z}=\mathrm{4} \\ $$$$\:{and}\:\mathrm{4}{x}+\mathrm{4}{y}+\mathrm{2}{z}=\mathrm{20}\:{which}\:{is}\:{in}\: \\ $$$${front}\:{of}\:{the}\:{region}\:{in}\:{the}\:{yz}\:{plane}\: \\ $$$${bounded}\:{by}\:{z}=\mathrm{2}{y}^{\mathrm{2}} \:{and}\:{z}=\sqrt{\mathrm{4}{y}} \\ $$
Question Number 189257 Answers: 1 Comments: 0
$$\boldsymbol{\mathrm{determine}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{surface}}\:\boldsymbol{\mathrm{area}}\: \\ $$$$\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{portion}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{z}}=\mathrm{13}−\mathrm{4}\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{4}\boldsymbol{\mathrm{y}}^{\mathrm{2}} \: \\ $$$$\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{above}}\:\boldsymbol{\mathrm{z}}=\mathrm{1}\:\boldsymbol{\mathrm{with}}\:\boldsymbol{\mathrm{x}}\leq\mathrm{0}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{y}}\geq\mathrm{0} \\ $$
Question Number 189256 Answers: 1 Comments: 0
$${Prove}\:{that} \\ $$$$\mathrm{sin10}°\:=\:\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\mathrm{2}−\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}−\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}−\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}−\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}−...........\infty}}}}}}}}}}}}} \\ $$
Question Number 189254 Answers: 1 Comments: 0
Question Number 189250 Answers: 0 Comments: 1
Question Number 189248 Answers: 2 Comments: 0
Question Number 189242 Answers: 0 Comments: 0
Question Number 189233 Answers: 1 Comments: 2
$$\mathrm{1}\bullet{Evaluer}\::\boldsymbol{{Aire}}\left(\boldsymbol{{A}}'\boldsymbol{{B}}'\boldsymbol{{C}}'\boldsymbol{{D}}'\right) \\ $$$$\mathrm{2}\bullet{En}\:{deduire}:\frac{\boldsymbol{{Aire}}\left(\boldsymbol{{A}}'\boldsymbol{{B}}'\boldsymbol{{C}}'\boldsymbol{{D}}'\right)}{\boldsymbol{{Aire}}\left(\boldsymbol{{ABCD}}\right)} \\ $$
Question Number 189223 Answers: 0 Comments: 2
$${who}\:{did}\:{discoer}\:{the}\:{light}'{s}\:{speed}\:{and} \\ $$$${by}\:{which}\:{method}? \\ $$
Question Number 189212 Answers: 0 Comments: 0
Question Number 189208 Answers: 2 Comments: 0
Question Number 189468 Answers: 2 Comments: 4
$$\:\:\:\mathrm{If}\:\mathrm{tan}\:\left(\frac{\mathrm{x}}{\mathrm{2}}\right)=\:\mathrm{csc}\:\mathrm{x}−\mathrm{sin}\:\mathrm{x}\:,\:\mathrm{then} \\ $$$$\:\:\mathrm{tan}\:^{\mathrm{2}} \left(\frac{\mathrm{x}}{\mathrm{2}}\right)=? \\ $$
Question Number 189465 Answers: 1 Comments: 0
Question Number 189464 Answers: 1 Comments: 0
Question Number 189201 Answers: 1 Comments: 0
$$\mathrm{In}\:\:\:\bigtriangleup\mathrm{ABC}\:\:\:\mathrm{holds}: \\ $$$$\sqrt{\mathrm{2}}\:\mathrm{a}\:\mathrm{cos}\:\frac{\mathrm{B}}{\mathrm{2}}\:\mathrm{cos}\:\frac{\mathrm{C}}{\mathrm{2}}\:=\:\mathrm{s} \\ $$$$\Rightarrow\:\mathrm{sec}\:\left(\mathrm{2B}\right)\:+\:\mathrm{tan}\:\left(\mathrm{2B}\right)\:=\:\frac{\mathrm{c}\:+\:\mathrm{b}}{\mathrm{c}\:−\:\mathrm{b}} \\ $$
Question Number 189189 Answers: 1 Comments: 0
Question Number 189183 Answers: 1 Comments: 0
Question Number 189174 Answers: 1 Comments: 0
$${log}_{\mathrm{3}} \left({x}+\mathrm{1}\right)=\mathrm{2}\:\:\:\:\:\:\:\:;\:\:\:{x}=? \\ $$
Question Number 189169 Answers: 1 Comments: 4
Question Number 189205 Answers: 0 Comments: 6
Question Number 189463 Answers: 1 Comments: 0
Question Number 189145 Answers: 6 Comments: 0
$${pleas}\:{solve}\:{this} \\ $$$$\left.\mathrm{1}\right)\:\:\:\:\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{{e}^{{x}+\mathrm{2}{x}+\mathrm{3}{x}+\mathrm{4}{x}+\centerdot\centerdot\centerdot\centerdot\centerdot+{nx}} −{e}^{\frac{{n}\left({n}+\mathrm{1}\right)}{\mathrm{2}}} }{{x}−\mathrm{1}}=? \\ $$$$\left.\mathrm{2}\right)\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{{e}^{\mathrm{2}^{{x}} \centerdot\mathrm{3}^{{x}} \centerdot\mathrm{4}^{{x}} \centerdot\centerdot\centerdot\centerdot{n}^{{x}} } −{e}^{{n}!} }{{x}−\mathrm{1}}=? \\ $$$$\left.\mathrm{3}\right)\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{{e}^{{x}+{x}^{\mathrm{2}} +{x}^{\mathrm{3}} +.......+{x}^{{n}} } −{e}^{{n}} }{{x}−\mathrm{1}}=? \\ $$
Question Number 189144 Answers: 0 Comments: 1
$$\: \\ $$$$\: \\ $$$$\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\sqrt{{x}\:+\:{y}\:+\:{z}}}{\:\sqrt{{x}}\:+\:\sqrt{{y}}\:+\:\sqrt{{z}}\:}\:{dxdydz} \\ $$$$\: \\ $$$$\: \\ $$
Question Number 189140 Answers: 2 Comments: 0
Question Number 189135 Answers: 2 Comments: 0
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