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Question Number 88238 Answers: 1 Comments: 0
$${solve}\: \\ $$$$\left(\mathrm{3}{x}^{\mathrm{5}} {y}^{\mathrm{4}} +\mathrm{4}{y}\right){dx}+\left(\mathrm{2}{x}^{\mathrm{6}} {y}^{\mathrm{3}} +\mathrm{3}{x}\right){dy}=\mathrm{0} \\ $$
Question Number 88236 Answers: 1 Comments: 0
$$\:\mathrm{Evaluate}\:\:\int\sqrt[{\mathrm{3}}]{\frac{\mathrm{27}}{{x}^{\mathrm{3}} −\mathrm{6}}}\:{dx}\: \\ $$
Question Number 88235 Answers: 0 Comments: 1
$$\:\mathrm{find}\:\mathrm{a}\:\mathrm{maclaurine}\:\mathrm{series}\:\mathrm{solution}\:\mathrm{to}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation} \\ $$$$\mathrm{up}\:\mathrm{to}\:\mathrm{the}\:\mathrm{term}\:\mathrm{in}\:{x}^{\mathrm{4}} . \\ $$$$\:\frac{{dy}}{{dx}}\:−\:{x}\:=\:{xy}\:\:\:\mathrm{if}\:\:{y}\:=\:\mathrm{1}\:\mathrm{when}\:{x}\:=\:\mathrm{0}. \\ $$
Question Number 88232 Answers: 0 Comments: 0
Question Number 88218 Answers: 1 Comments: 2
Question Number 88214 Answers: 2 Comments: 0
Question Number 88212 Answers: 0 Comments: 0
$$\Sigma\left[\left(\mathrm{e}^{\mathrm{s}^{\mathrm{e}^{\mathrm{s}^{} } } } −\mathrm{x}\right)^{\mathrm{r}} \right]^{\left(\mathrm{s}+\mathrm{5}\right)\frac{\mathrm{sin}\:{x}}{\mathrm{tan}\:{y}}} \:={i} \\ $$$${s}=\mathrm{5} \\ $$$$\mathrm{r}=\mathrm{2} \\ $$$${x}=\mathrm{90}° \\ $$$$ \\ $$$$\mathrm{y}=\mathrm{45}° \\ $$$$\mathrm{i}=? \\ $$$$ \\ $$
Question Number 88211 Answers: 0 Comments: 0
Question Number 88210 Answers: 1 Comments: 0
$$\mathrm{If}\:{f}\left({x}\right)=\begin{cases}{\mathrm{1}−{x},\:\:\:\:\:\:\:\:\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}}\\{\mathrm{0},\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}\leqslant{x}\leqslant\mathrm{2}\:\:\:\:}\\{\left(\mathrm{2}−{x}\right)^{\mathrm{2}} ,\:\:\:\mathrm{2}\leqslant{x}\leqslant\mathrm{3}}\end{cases}\:\mathrm{and}\: \\ $$$$\phi\left({x}\right)=\underset{\:\mathrm{0}} {\overset{\mathrm{x}} {\int}}\:{f}\left({t}\right)\:{dt}.\:\mathrm{Then}\:\mathrm{for}\:\mathrm{any}\:{x}\:\in\:\left[\mathrm{2},\:\mathrm{3}\right],\: \\ $$$$\phi\left({x}\right)\:= \\ $$
Question Number 88207 Answers: 1 Comments: 1
$${what}\:{is}\:{the}\:{biggest}\:{prime}\:{p}\:{verifying}: \\ $$$${p}=\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\left[\sqrt{{k}}\right] \\ $$$${where}\:{n}\in\mathbb{N}\:\mathrm{and}\:\:\left[{x}\right]\:{is}\:{floor}\left({x}\right) \\ $$
Question Number 88206 Answers: 1 Comments: 0
$$\int\:\:\frac{\mathrm{x}+\mathrm{x}^{\mathrm{3}} }{\mathrm{1}+\mathrm{x}^{\mathrm{4}} }\:\mathrm{dx}\: \\ $$
Question Number 88204 Answers: 0 Comments: 0
$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{radi}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{circle}}\left(\boldsymbol{\mathrm{s}}\right)\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{tangents}} \\ $$$$\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{corves}}\::\begin{cases}{\boldsymbol{\mathrm{y}}=\boldsymbol{\mathrm{x}}\pm\frac{\mathrm{1}}{\boldsymbol{\mathrm{y}}^{\mathrm{2}} }}\\{\boldsymbol{\mathrm{x}}=\boldsymbol{\mathrm{y}}\pm\frac{\mathrm{1}}{\boldsymbol{\mathrm{x}}^{\mathrm{2}} }}\end{cases} \\ $$
Question Number 88203 Answers: 0 Comments: 0
$$\boldsymbol{\mathrm{y}}=\boldsymbol{\mathrm{ax}}^{−\mathrm{3}} ,\:\boldsymbol{\mathrm{meets}}:\:\:\boldsymbol{\mathrm{y}}=\boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{x}}} \:\:\boldsymbol{\mathrm{and}}\:\:\boldsymbol{\mathrm{y}}=−\boldsymbol{\mathrm{e}}^{−\boldsymbol{\mathrm{x}}} \:\boldsymbol{\mathrm{at}}: \\ $$$$\boldsymbol{\mathrm{A}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{B}},\boldsymbol{\mathrm{such}}\:\boldsymbol{\mathrm{that}}:\:\boldsymbol{\mathrm{AB}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{minimum}}. \\ $$$$\boldsymbol{\mathrm{find}}:\:\boldsymbol{\mathrm{possible}}\:\boldsymbol{\mathrm{value}}\left(\boldsymbol{\mathrm{s}}\right)\:\boldsymbol{\mathrm{of}}:\:\boldsymbol{\mathrm{a}}\:\:\:\boldsymbol{\mathrm{and}}\:\:\boldsymbol{\mathrm{min}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{AB}}. \\ $$
Question Number 88198 Answers: 1 Comments: 0
$$\mathrm{Factorize}\:\:−{r}^{\mathrm{2}} +{p}^{\mathrm{2}} +{q}^{\mathrm{2}} −\mathrm{2}{pq}\:. \\ $$
Question Number 88197 Answers: 0 Comments: 0
$${prove}\:{that}\: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\frac{{x}^{\mathrm{2}} −\mathrm{2}}{{x}^{\mathrm{2}} −\mathrm{1}}\:}{dx}=\frac{\pi\sqrt{\mathrm{2}\pi}}{\Gamma^{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{4}}\right)}+\frac{\Gamma^{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{4}}\right)}{\mathrm{4}\sqrt{\mathrm{2}\pi}} \\ $$
Question Number 88196 Answers: 0 Comments: 0
Question Number 88194 Answers: 0 Comments: 4
$${find}\:\int\frac{\mathrm{1}}{\sqrt{{x}}+\sqrt{{x}+\mathrm{1}}+\sqrt{{x}+\mathrm{2}}}\:{dx} \\ $$$$ \\ $$
Question Number 88188 Answers: 1 Comments: 5
Question Number 88181 Answers: 0 Comments: 1
Question Number 88180 Answers: 0 Comments: 0
$$\left(\mathrm{5}+\mathrm{4}{y}\right)×{dy}={y}^{\mathrm{3}} {x}\: \\ $$
Question Number 88179 Answers: 1 Comments: 0
$${z}={x}^{\mathrm{2}} /{y}^{\mathrm{3}} \:\:\:\:\:\:\:\:\:\:{dz}=? \\ $$
Question Number 88178 Answers: 0 Comments: 0
$$ \\ $$
Question Number 88177 Answers: 1 Comments: 0
$${prove}\:{that} \\ $$$$ \\ $$$$\int_{\mathrm{0}} ^{\mathrm{2020}} \left({x}−\left[{x}\right]\right)\sqrt{{x}−\left[{x}\right]}\:{dx}=\mathrm{808} \\ $$
Question Number 88170 Answers: 0 Comments: 2
$${Prove}\:{that}\: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} {tcos}\:{n}\pi{tdt}=\frac{\left(−\mathrm{1}\right)^{{n}} −\mathrm{1}}{{n}^{\mathrm{2}} \pi^{\mathrm{2}} } \\ $$
Question Number 88169 Answers: 1 Comments: 2
$$\mathrm{find}\:\mathrm{Laplace}\:\mathrm{transform}\: \\ $$$$\mathrm{t}^{\mathrm{3}} .\:\mathrm{cos}\:\:\mathrm{4t} \\ $$
Question Number 88160 Answers: 2 Comments: 1
$${solve}\::\:{x}^{\mathrm{2}} \:=\:\mathrm{3}{x}\:+\:\mathrm{6}{y}\:;\:{xy}\:=\:\mathrm{5}{x}\:+\:\mathrm{4}{y} \\ $$
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