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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
$${solve}\::\:{x}^{\mathrm{2}} \:=\:\mathrm{3}{x}\:+\:\mathrm{6}{y}\:;\:{xy}\:=\:\mathrm{5}{x}\:+\:\mathrm{4}{y} \\ $$
Question Number 88153 Answers: 0 Comments: 1
Question Number 88141 Answers: 1 Comments: 0
Question Number 88137 Answers: 1 Comments: 2
$${Mr}\:{mjs}\: \\ $$$${x},\:\mathrm{3},\mathrm{7},\mathrm{13},\mathrm{27},\mathrm{33},{y} \\ $$$${find}\:{x}\:\&\:{y}\:?\:{any}\:{formula} \\ $$$${to}\:{generally}? \\ $$
Question Number 88131 Answers: 1 Comments: 0
$$\int\frac{{x}^{\mathrm{2}} +\mathrm{1}}{{x}−\sqrt{\mathrm{1}−\mathrm{2}{x}}}{dx} \\ $$
Question Number 91093 Answers: 0 Comments: 16
$${dear}\:{admint}\: \\ $$$${Tinkutara}.\:{why}\:{my}\:{phone} \\ $$$${nothing}\:{have}\:{notification}\:{sir}? \\ $$$$ \\ $$
Question Number 88128 Answers: 1 Comments: 0
$${given}\:\mathrm{27}^{{a}} \:=\:\mathrm{64}^{{b}} \:=\:\mathrm{216}^{{c}} \:=\:\mathrm{72} \\ $$$${find}\:\frac{\mathrm{2020}{abc}}{\mathrm{3}{ab}+\mathrm{3}{ac}+\mathrm{3}{bc}}\:+\:\frac{{ab}+{ac}+{bc}}{\mathrm{2020}{abc}} \\ $$
Question Number 88118 Answers: 1 Comments: 1
$$\int\frac{\mathrm{dx}}{\left(\mathrm{x}+\mathrm{1}\right)×\sqrt{\mathrm{x}}} \\ $$
Question Number 88104 Answers: 1 Comments: 2
$$\int_{\mathrm{0}} ^{+\infty} \sqrt{\mathrm{3}+{e}^{−\mathrm{2}{x}} }{dx} \\ $$
Question Number 88101 Answers: 0 Comments: 0
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