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Question Number 84574 Answers: 0 Comments: 1
$${calculate}\:\:{I}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:{sin}\left({narcsinx}\right){dx} \\ $$
Question Number 84572 Answers: 0 Comments: 0
$${let}\:\:{F}\left({z}\right)\:=\frac{{z}^{\mathrm{2}} }{\mathrm{1}+{z}^{\mathrm{7}} } \\ $$$$\left.\mathrm{1}\right)\:{factorize}\:{inside}\:{C}\left[{x}\right]\:{and}\:{R}\left[{x}\right] \\ $$$${z}^{\mathrm{7}} \:+\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{decompose}\:{inside}\:{C}\left({x}\right){and}\:{R}\left({x}\right) \\ $$$${the}\:{fraction}\:{F}\left({x}\right) \\ $$
Question Number 84571 Answers: 0 Comments: 0
$${calculate}\:{S}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\left(−\mathrm{1}\right)^{{k}} }{\sqrt{{k}}} \\ $$
Question Number 84570 Answers: 1 Comments: 1
$${calculate}\:\int_{\mathrm{1}} ^{+\infty} \:\frac{{arctan}\left(\frac{\mathrm{3}}{{x}}\right)}{{x}^{\mathrm{2}} }{dx} \\ $$
Question Number 84569 Answers: 1 Comments: 0
$${find}\:\:\int\:\:\:\:\frac{{dx}}{\mathrm{1}+{tan}^{\mathrm{4}} {x}} \\ $$
Question Number 84568 Answers: 0 Comments: 4
$$\mathrm{without}\:\mathrm{L}'\mathrm{hopital} \\ $$$$\underset{{x}\rightarrow−\frac{\mathrm{1}}{\mathrm{2}}} {\mathrm{lim}}\:\frac{\mathrm{2x}^{\mathrm{3}} +\mathrm{3x}^{\mathrm{2}} −\sqrt{\mathrm{a}+\mathrm{bx}}}{\mathrm{4x}^{\mathrm{2}} −\mathrm{1}}\:=\:−\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$\mathrm{find}\:\mathrm{a}+\mathrm{b} \\ $$
Question Number 84566 Answers: 0 Comments: 0
Question Number 84564 Answers: 0 Comments: 1
$$\mathrm{find}\:\mathrm{arg}\left(\mathrm{z}\right)\:\mathrm{given}\:\mathrm{that}\:\:\mathrm{z}\:=\:\frac{\mathrm{1}\:+\:{i}}{\mathrm{1}−{i}} \\ $$
Question Number 84561 Answers: 1 Comments: 0
$$\int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{\infty} \frac{{cos}\left({x}−{y}\right)−{cos}\left({x}\right)}{{xy}}{dx}\:{dy} \\ $$
Question Number 84558 Answers: 0 Comments: 1
$${happy}\:\pi\:{day} \\ $$
Question Number 84557 Answers: 0 Comments: 1
Question Number 84556 Answers: 1 Comments: 1
$$\int\:\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{2x}+\mathrm{2}}{\sqrt{\mathrm{4x}^{\mathrm{2}} +\mathrm{8x}+\mathrm{13}}}\right)\:\mathrm{dx} \\ $$
Question Number 84553 Answers: 0 Comments: 3
$${Find}\:\:{mininum}\:\:{value}\:\:{of}\:\:{n}\:\:{such}\:\:{that} \\ $$$${both}\:\:{n}\:+\:\mathrm{3}\:\:\:{and}\:\:\mathrm{2020}{n}\:+\:\mathrm{1}\:\:{are}\:\:{square}\:\:{numbers}\:. \\ $$
Question Number 84549 Answers: 1 Comments: 0
Question Number 84544 Answers: 0 Comments: 0
$${solve}\: \\ $$$${xy}^{''} ={y}^{'} \left({e}^{{y}} −\mathrm{1}\right) \\ $$
Question Number 84543 Answers: 0 Comments: 3
$$\boldsymbol{\mathrm{Determine}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}}\:,\boldsymbol{\mathrm{c}}\:\:\boldsymbol{\mathrm{so}}\:\boldsymbol{\mathrm{that}} \\ $$$$\:\:\underset{\mathrm{x}\rightarrow\mathrm{0}} {\overset{\mathrm{lim}} {\:}}\:\frac{\left(\boldsymbol{\mathrm{a}}\:+\boldsymbol{\mathrm{b}}\:\mathrm{cos}\:\mathrm{x}\right)\:\mathrm{x}−\boldsymbol{\mathrm{c}}\:\mathrm{sin}\:\mathrm{x}}{\mathrm{x}^{\mathrm{5}} }=\mathrm{1} \\ $$
Question Number 84532 Answers: 1 Comments: 1
$$\mathrm{x}>\:\mathrm{0}\:,\:\mathrm{y}\:>\:\mathrm{0}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\frac{\mathrm{xy}}{\mathrm{x}+\mathrm{y}}\:<\:\mathrm{x} \\ $$
Question Number 84531 Answers: 1 Comments: 2
$$\mathrm{find}\:\mathrm{for}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{image}\:\mathrm{ellipse} \\ $$$$\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{9}}\:+\:\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{8}}\:=\:\mathrm{1}\:\mathrm{if}\:\mathrm{reflected}\:\mathrm{with}\:\mathrm{line} \\ $$$$\mathrm{x}\:+\:\mathrm{y}\:=\:−\mathrm{4} \\ $$
Question Number 84528 Answers: 0 Comments: 3
$$\mathrm{1}=\mathrm{2} \\ $$
Question Number 84515 Answers: 1 Comments: 0
$${Q}.{solve} \\ $$$${x}^{\mathrm{3}} −{x}={x}! \\ $$
Question Number 84512 Answers: 1 Comments: 0
Question Number 84510 Answers: 2 Comments: 0
Question Number 84505 Answers: 0 Comments: 1
$$\left.\mathrm{2}\right){calculate}\:\:\:{I}\left(\xi\right)\:=\int_{\xi} ^{\mathrm{1}} \:\:\:\:\:\:\frac{{dx}}{\sqrt{\mathrm{1}+\xi{x}^{\mathrm{2}} −\sqrt{\mathrm{1}−\xi{x}^{\mathrm{2}} }}} \\ $$$$\left.\mathrm{1}\right){find}\:{lim}_{\xi\rightarrow\mathrm{0}} \:\:{I}\left(\xi\right) \\ $$
Question Number 84498 Answers: 0 Comments: 1
$$\int\sqrt{{x}}\:{cos}\sqrt{{x}}\:{dx} \\ $$
Question Number 84497 Answers: 0 Comments: 1
$$\int\frac{{x}^{\mathrm{2}} }{\mathrm{1}+{x}^{\mathrm{5}} }\:{dx} \\ $$$$ \\ $$
Question Number 84496 Answers: 1 Comments: 1
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