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Question Number 143576 Answers: 0 Comments: 0
$${find}\:{L}\left(\frac{{arctanx}}{{x}}\right) \\ $$
Question Number 143575 Answers: 1 Comments: 0
$${find}\:{L}\left({e}^{−\sqrt{{x}}} \right) \\ $$
Question Number 143570 Answers: 1 Comments: 0
Question Number 143715 Answers: 0 Comments: 0
$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \mathrm{tanx}\centerdot\mathrm{Li}\left(\mathrm{tan}^{\mathrm{2}} \mathrm{x}\right)\mathrm{dx} \\ $$
Question Number 143562 Answers: 0 Comments: 0
Question Number 143561 Answers: 3 Comments: 0
$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{1}−\frac{\mathrm{2}}{{x}^{} }+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)^{{x}} =? \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\sqrt{{n}}−\sqrt{{n}−\mathrm{1}}\right)\sqrt{{n}+\mathrm{1}}\:=? \\ $$
Question Number 143556 Answers: 0 Comments: 0
$$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{dx}}{\mathrm{x}^{\alpha} \left(\mathrm{lnx}\right)^{\beta} } \\ $$
Question Number 143546 Answers: 1 Comments: 0
$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{log}^{\mathrm{2}} \mathrm{x}}{\left(\mathrm{8}+\mathrm{x}^{\mathrm{4}} \right)^{\mathrm{2}} }\mathrm{dx} \\ $$
Question Number 143542 Answers: 0 Comments: 0
$${calculate}\:{the}\:{polar}\:{integral}\:{that} \\ $$$$\:{give}\:{the}\:{area}\:{of}\:{the}\:{region}\:{bunded}\:{by}\:{the}\:{curves}\: \\ $$$$ \\ $$$${r}=\mathrm{2}\:,{r}=\mathrm{4}{cos}\theta\:{and}\:,{r}\:{cos}\theta=\mathrm{3}\: \\ $$$$ \\ $$
Question Number 143531 Answers: 1 Comments: 0
$$\:\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\:\frac{\mathrm{2}\sqrt{{x}}+\mathrm{3}\:\sqrt[{\mathrm{3}}]{{x}}\:+\mathrm{5}\:\sqrt[{\mathrm{5}}]{{x}}}{\:\sqrt{\mathrm{3}{x}−\mathrm{2}}\:+\sqrt[{\mathrm{3}}]{\mathrm{2}{x}−\mathrm{3}}}\:=? \\ $$
Question Number 143532 Answers: 1 Comments: 0
$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:\mathrm{cos}\:{x}}{\mathrm{tan}\:^{\mathrm{4}} {x}}\:=? \\ $$
Question Number 143523 Answers: 1 Comments: 0
$${Determiner}\:{l}'{origine}\:{de}\:{laplace} \\ $$$$\mathrm{1}−{F}\left({p}\right)=\frac{{p}}{\left({p}+\mathrm{2}\right)^{\mathrm{2}} } \\ $$
Question Number 143521 Answers: 0 Comments: 1
Question Number 143519 Answers: 3 Comments: 0
$$ \\ $$$${The}\:{first}\:{two}\:{terms}\:{of}\:{the}\:\left\{{a}_{{n}} \right\}\:{series}\:\:\:{are}\:{defind}\:{as}\:{a}_{{n}} ={a}_{{n}−\mathrm{1}} +{a}_{{n}−\mathrm{2}} \:\:{for}\:{the}\:{general}\:{term} \\ $$$$\:{a}_{\mathrm{1}} =\mathrm{5},\:{a}_{\mathrm{2}} =\mathrm{8}\:{and}\:{n}\geqslant\mathrm{3}\:. \\ $$$${since}\:{the}\:{L}={li}\underset{{n}\rightarrow\infty} {{m}}\frac{{a}_{{n}+\mathrm{1}} }{{a}_{{n}} }\:\:{what}\:{is}\:{the}\:{value}\:{of}\:{L} \\ $$$$ \\ $$
Question Number 143516 Answers: 2 Comments: 1
Question Number 143508 Answers: 3 Comments: 0
$$ \\ $$$$\:\:\:\:\:\:\:\:..........{Calculus}........ \\ $$$$\:\:\:\:{i}:\:\:\:\boldsymbol{\phi}_{\mathrm{1}} :=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}^{\mathrm{2}} \left(\mathrm{1}−{x}\right).{ln}\left({x}\right)}{{x}}{dx} \\ $$$$\:\:\:{ii}:\:\:\:\boldsymbol{\phi}_{\mathrm{2}} :=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}^{\mathrm{2}} \left({x}\right).{ln}\left(\mathrm{1}−{x}\right)}{{x}}\:{dx} \\ $$$$\:\:{iii}\::\:\boldsymbol{\phi}_{\mathrm{3}} \::=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}^{\mathrm{2}} \left({x}\right).{ln}\left(\mathrm{1}+{x}\right)}{{x}}{dx} \\ $$
Question Number 143507 Answers: 1 Comments: 0
$$\mathrm{10}\sqrt{\mathrm{20}}+\mathrm{13}\sqrt{\mathrm{45}} \\ $$
Question Number 143506 Answers: 1 Comments: 0
$$\underset{\mathrm{1}} {\overset{\infty} {\int}}\frac{\mathrm{1}}{{e}^{−{x}} +{e}^{{x}} }\:{dx}=? \\ $$$$ \\ $$
Question Number 143505 Answers: 1 Comments: 1
Question Number 143501 Answers: 0 Comments: 0
Question Number 143502 Answers: 0 Comments: 0
Question Number 143499 Answers: 1 Comments: 1
Question Number 143514 Answers: 0 Comments: 1
Question Number 143495 Answers: 1 Comments: 0
$${On}\:{definit}\:{la}\:{fonction}\: \\ $$$$\mathscr{L}\left({f}\left({t}\right)\right)\left({p}\right)=\int_{\mathrm{0}} ^{+\infty} {f}\left({t}\right){e}^{−{pt}} {dt} \\ $$$${Calculer}\:\mathscr{L}\left(\left(\frac{{t}^{{n}} }{{n}!}\right)\right)\left({p}\right) \\ $$
Question Number 143493 Answers: 0 Comments: 1
Question Number 143491 Answers: 0 Comments: 1
$$\mathrm{Find}\:\underset{\mathrm{n}\rightarrow+\propto} {\mathrm{lim}}\left(\mathrm{u}_{\mathrm{n}} \right),\mathrm{If}\:\begin{cases}{\mathrm{u}_{\mathrm{0}} =\mathrm{1},\mathrm{n}=\mathrm{1},\mathrm{2},\mathrm{3},.....}\\{\mathrm{u}_{\mathrm{n}} =\:\frac{\mathrm{2018}}{\mathrm{2019}}\mathrm{u}_{\mathrm{n}−\mathrm{1}} +\:\frac{\mathrm{1}}{\left(\mathrm{u}_{\mathrm{n}−\mathrm{1}} \right)^{\mathrm{2018}} }}\end{cases} \\ $$
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