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Question Number 149775 Answers: 0 Comments: 2
$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\mathrm{5}^{\boldsymbol{\mathrm{x}}} \:=\:\left(\mathrm{3}^{\boldsymbol{\mathrm{x}}} \:−\:\mathrm{2}^{\boldsymbol{\mathrm{x}}} \right)^{\mathrm{2}} \\ $$
Question Number 149773 Answers: 1 Comments: 0
Question Number 149772 Answers: 0 Comments: 0
Question Number 150095 Answers: 1 Comments: 0
$$\Omega\:=\int\:\frac{\mathrm{x}\:\mathrm{dx}}{\mathrm{x}^{\mathrm{8}} \:-\:\mathrm{1}}\:=\:? \\ $$
Question Number 149770 Answers: 0 Comments: 2
$$\mathrm{6}\boldsymbol{{z}}^{\mathrm{4}} \:=\:\boldsymbol{{z}}^{\boldsymbol{{z}}^{\mathrm{2}} } \:\:\Rightarrow\:\:\mathrm{1}\:+\:\boldsymbol{{z}}^{\mathrm{2}} \:+\:\boldsymbol{{z}}^{\mathrm{4}} \:=\:? \\ $$
Question Number 149768 Answers: 0 Comments: 0
Question Number 149766 Answers: 1 Comments: 2
$$\mathrm{Find}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{x}\:+\:\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{x}\:+\:\mathrm{1}}\:=\:\frac{\mathrm{10}}{\mathrm{3}} \\ $$
Question Number 149757 Answers: 0 Comments: 1
Question Number 149739 Answers: 3 Comments: 0
Question Number 149731 Answers: 0 Comments: 2
Question Number 149733 Answers: 1 Comments: 0
Question Number 149720 Answers: 1 Comments: 0
Question Number 149718 Answers: 1 Comments: 0
Question Number 149686 Answers: 2 Comments: 2
Question Number 149675 Answers: 0 Comments: 0
$$\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\sqrt[{\boldsymbol{\mathrm{n}}}]{\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} \:+\:\frac{\mathrm{1}}{\mathrm{4}}\right)^{\boldsymbol{\mathrm{n}}+\mathrm{1}} }}\:=\:? \\ $$
Question Number 149673 Answers: 3 Comments: 0
$$\:\:\:\mathrm{solve}\::: \\ $$$$\left[\:\mathrm{1}\right]\:\:\:\:\boldsymbol{\phi}\::=\:\int_{\mathrm{0}} ^{\:\:\infty\:} \frac{{ln}^{\:\mathrm{2}} \:\left({e}\:{x}\:\right)}{{e}^{\:\mathrm{4}} \:+{x}^{\:\mathrm{2}} }\:{dx}\:=\frac{\pi\:{k}}{{e}^{\:\mathrm{2}} } \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{k}:=\:? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\left[\:\mathrm{2}\:\right]\:\:\:\Omega\::=\:\int_{\mathrm{0}\:} ^{\:\infty} \:\frac{\:{ln}^{\:\mathrm{3}} \:\left({x}\:\right)}{\:{e}^{\:\mathrm{2}} +\:{x}^{\:\mathrm{2}} }\:{dx}\:=\:? \\ $$
Question Number 149670 Answers: 1 Comments: 0
$$\:\:\:{Solve}\:{the}\:{equation}\: \\ $$$$\:\:{x}=\sqrt{{a}−\sqrt{{a}+{x}}\:}\:{where}\:{a}>\mathrm{0}\:{is}\: \\ $$$$\:{a}\:{parameter}. \\ $$
Question Number 149667 Answers: 2 Comments: 0
$$\: \\ $$$${f}\:\left({x}\:\right)=\:\frac{\mathrm{1}}{\:\sqrt{\:\mathrm{1}\:+\:{sin}\:\left({x}\:\right)}\:+\sqrt{\:\mathrm{1}\:+\:{cos}\:\left({x}\right)}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{find}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Min}\left(\:{f}\:\left({x}\right)\right)\:=? \\ $$$$ \\ $$
Question Number 149660 Answers: 1 Comments: 0
Question Number 150362 Answers: 1 Comments: 0
$$\mathrm{Given}\:\mathrm{that}\:\mathrm{p}=\left(\mathrm{3i}+\mathrm{4j}\right)\:,\:\mathrm{q}=\left(\mathrm{2i}−\mathrm{j}\right)\:\mathrm{and} \\ $$$$\mathrm{r}=\mathrm{5i}−\mathrm{j}.\:\mathrm{Express}\:\:\mathrm{vector}\:\:\:\mathrm{r}\:\:\mathrm{intrems}\:\mathrm{of} \\ $$$$\mathrm{p}\:\mathrm{and}\:\mathrm{q}\:. \\ $$
Question Number 149638 Answers: 0 Comments: 0
Question Number 149637 Answers: 2 Comments: 0
Question Number 149636 Answers: 1 Comments: 0
Question Number 149634 Answers: 1 Comments: 0
$$\mathrm{Trouver}\:\mathrm{toutes}\:\mathrm{les}\:\mathrm{fonctions}\:\mathrm{f}:\mathbb{N}\rightarrow\mathbb{R}^{+} \\ $$$$\mathrm{telque}\:\forall\left(\mathrm{a},\mathrm{b}\right)\in\mathbb{N}, \\ $$$$\mathrm{f}\left(\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} \right)=\mathrm{f}\left(\mathrm{a}^{\mathrm{2}} \right)+\mathrm{f}\left(\mathrm{b}^{\mathrm{2}} \right)\:\mathrm{et}\:\mathrm{f}\left(\mathrm{1}\right)=\mathrm{1} \\ $$
Question Number 152856 Answers: 0 Comments: 2
$$\mathrm{Monsieur}\:\mathrm{Puissant},\:\mathrm{je}\:\mathrm{quitte}\:\mathrm{ce}\:\mathrm{forum} \\ $$$$\mathrm{math}\acute {\mathrm{e}matique}\:\mathrm{d}\acute {\mathrm{e}finitivement}\:\mathrm{mais} \\ $$$$\mathrm{sans}\:\mathrm{avoir}\:\mathrm{dit}\:\mathrm{que}\:\mathrm{j}'\mathrm{ai}\:\mathrm{ador}\acute {\mathrm{e}}\:\acute {\mathrm{e}changer} \\ $$$$\mathrm{avec}\:\mathrm{vous}. \\ $$$$ \\ $$$$\mathrm{Bonne}\:\mathrm{continuation}\:\mathrm{et}\:\mathrm{vive}\:\mathrm{les} \\ $$$$\mathrm{maths}\:! \\ $$
Question Number 152601 Answers: 2 Comments: 1
$$ \\ $$$$\:\:\:{solve}.... \\ $$$$\:\:{lim}_{\:{n}\rightarrow\infty} \left\{\:\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}\left(\mathrm{1}\:−\frac{{k}}{{n}}+\frac{{k}^{\:\mathrm{2}} }{{n}^{\:\mathrm{2}} }\:\right)^{\:\frac{\mathrm{1}}{{n}}} \right\}=? \\ $$$$\:\:{m}.{n}... \\ $$$$ \\ $$
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