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Question Number 155992 Answers: 0 Comments: 0
$$\:\left(\mathrm{1}+\mathrm{log}\:_{\mathrm{3}} \:\mathrm{x}\right).\sqrt{\mathrm{log}\:_{\mathrm{3x}} \:\sqrt[{\mathrm{3}}]{\frac{\mathrm{x}}{\mathrm{3}}}}\:\leqslant\:\mathrm{2} \\ $$
Question Number 155991 Answers: 2 Comments: 1
$$\:\begin{cases}{\mathrm{a}\left(\mathrm{x}+\mathrm{2}\right)+\mathrm{y}=\mathrm{3a}}\\{\mathrm{a}+\mathrm{2x}^{\mathrm{3}} =\mathrm{y}^{\mathrm{3}} +\left(\mathrm{a}+\mathrm{2}\right)\mathrm{x}^{\mathrm{3}} }\end{cases} \\ $$$$\:\mathrm{solve}\:\mathrm{for}\:\mathrm{x}\:\&\mathrm{y}\:\mathrm{in}\:\mathrm{term}\:\mathrm{a} \\ $$
Question Number 155989 Answers: 0 Comments: 1
$$\:\:\:\:\mathrm{5sin}\:^{\mathrm{2}} \mathrm{2x}\:+\:\mathrm{8cos}\:^{\mathrm{3}} \mathrm{x}\:=\:\mathrm{8cos}\:\mathrm{x} \\ $$$$\:\:\:\:\frac{\mathrm{3}\pi}{\mathrm{2}}\leqslant\mathrm{x}\leqslant\mathrm{2}\pi \\ $$
Question Number 155988 Answers: 2 Comments: 0
$$\mathrm{2}^{\overset{} {\mathrm{2}}} \\ $$
Question Number 155986 Answers: 0 Comments: 0
Question Number 155984 Answers: 0 Comments: 0
Question Number 155983 Answers: 1 Comments: 2
$$\:{given}\:\:{y}=\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}}\:,\:{then} \\ $$$$\:\left(\mathrm{1}−{x}^{\mathrm{2}} \right)\frac{{dy}}{{dx}}+\boldsymbol{{k}}{y}=\mathrm{0}.\:{find}\:\boldsymbol{{k}} \\ $$
Question Number 156105 Answers: 1 Comments: 0
$$\mathrm{Find}\:\mathrm{The}\:\mathrm{derivatif}\:\mathrm{of}\:\mathrm{this}\:\mathrm{function}: \\ $$$$\left.\mathrm{1}\right).\:\:\mathrm{y}^{\mathrm{4}} +\mathrm{3y}−\mathrm{4x}^{\mathrm{3}} =\mathrm{5x}+\mathrm{1} \\ $$$$\left.\mathrm{2}\right).\:\:\mathrm{4xy}^{\mathrm{3}} −\mathrm{x}^{\mathrm{2}} \mathrm{y}+\mathrm{x}^{\mathrm{3}} −\mathrm{5x}+\mathrm{6}=\mathrm{0} \\ $$$$\left.\mathrm{3}\right).\:\:\mathrm{3y}^{\mathrm{4}} +\mathrm{4x}−\mathrm{x}^{\mathrm{2}} \mathrm{sin}\:\mathrm{y}−\mathrm{4}=\mathrm{0} \\ $$$$\left.\mathrm{4}\right).\:\mathrm{y}=\mathrm{x}^{\mathrm{2}} \mathrm{sin}\:\mathrm{y} \\ $$$$\left.\mathrm{5}\right).\:\:\mathrm{sin}^{\mathrm{2}} \:\mathrm{3y}=\mathrm{x}+\mathrm{y}−\mathrm{1} \\ $$$$\: \\ $$
Question Number 155977 Answers: 0 Comments: 0
Question Number 155972 Answers: 0 Comments: 0
Question Number 155973 Answers: 1 Comments: 2
$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{3}} −\mathrm{3x}^{\mathrm{2}} +\mathrm{4x}−\mathrm{1} \\ $$$$\mathrm{find}\:\mathrm{a}=? \\ $$$$\mathrm{whenever}\:\:\:\:\mathrm{f}\left(\mathrm{a}\right)=\mathrm{f}^{−\mathrm{1}} \left(\mathrm{a}\right) \\ $$$$ \\ $$
Question Number 155969 Answers: 1 Comments: 0
Question Number 155965 Answers: 1 Comments: 0
$$\left({x}\:\mathrm{sin}\:\frac{{y}}{{x}}−{y}\:\mathrm{cos}\:\frac{{y}}{{x}}\right){dx}+{x}\:\mathrm{cos}\:\frac{{y}}{{x}}\:{dy}=\mathrm{0} \\ $$
Question Number 155959 Answers: 1 Comments: 0
$${quel}\:{est}\:{le}\:{changement}\:{de}\:{variable}\:{qui}\:{permet}\:{de}\:{passer} \\ $$$${de}\:{l}'{equation}\:{differentielle}\:: \\ $$$${x}^{\mathrm{2}} {y}''−\mathrm{3}{xy}'+\mathrm{4}{y}=\mathrm{0} \\ $$$${a}\:{une}\:{equation}\:{lineaire}\:{d}'{ordre}\:\mathrm{2}\:\:{coefficient}\:{comstant}\:\:{en}\:{z} \\ $$
Question Number 159716 Answers: 1 Comments: 0
$${Show}\:{that}\:\bigtriangledown{r}^{{n}} ={nr}^{{n}−\mathrm{2}} {r} \\ $$
Question Number 155951 Answers: 1 Comments: 0
$$ \\ $$$$\:\:\:\:\:\:\:{solve}\:\:: \\ $$$$ \\ $$$$\:\:\:\:\:\lfloor\:\frac{\mathrm{1}}{{x}}\:\rfloor\:+\:\lfloor\:\frac{\mathrm{3}}{{x}}\:\rfloor=\:\mathrm{4}\: \\ $$$$ \\ $$
Question Number 155945 Answers: 1 Comments: 1
Question Number 155937 Answers: 0 Comments: 1
$$\:\underset{\mathrm{a}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\mathrm{3a}}\:\sqrt{\mathrm{cos}\:\mathrm{2a}}\:\mathrm{cos}\:\mathrm{a}}{\mathrm{a}\:\mathrm{sin}\:\mathrm{a}\:\mathrm{cos}\:\mathrm{2a}}\:=? \\ $$
Question Number 155933 Answers: 0 Comments: 1
$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\int_{−\infty} ^{\:\infty} \:\frac{\sqrt{\mathrm{1}+\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}\:}\:}{{x}^{\mathrm{2}} +\:{x}\:+\mathrm{1}}\:{dx} \\ $$$$\: \\ $$
Question Number 155930 Answers: 1 Comments: 2
$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\:\frac{\mathrm{sin}\left({x}\right)\mathrm{cos}\left({x}\right)}{\mathrm{sin}^{\mathrm{3}} \left({x}\right)+\mathrm{cos}^{\mathrm{3}} \left({x}\right)}\:{dx} \\ $$$$\: \\ $$
Question Number 155929 Answers: 0 Comments: 0
$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{1}} ^{\:\mathrm{2}} \:\frac{\sqrt{{x}^{\mathrm{2}} }}{\mathrm{ln}\left({x}^{\mathrm{2}} \right)}\:{dx} \\ $$$$\: \\ $$
Question Number 155928 Answers: 1 Comments: 0
Question Number 155927 Answers: 0 Comments: 1
Question Number 155919 Answers: 1 Comments: 0
Question Number 155918 Answers: 0 Comments: 1
$$\mathrm{Can}\:\mathrm{you}\:\mathrm{evaluate}\:\mathrm{this}\:\mathrm{sum}? \\ $$$$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\mathrm{2}^{−\mathrm{n}} \mathrm{tan}\:\left(\mathrm{2}^{−\mathrm{n}} \right) \\ $$
Question Number 155914 Answers: 0 Comments: 0
$${D}\mathrm{raw}\:\mathrm{the}\:\mathrm{Newman}\:\mathrm{projection}\:\mathrm{formula} \\ $$$$\mathrm{for}\:\mathrm{the}\:\mathrm{chair}\:\mathrm{conformation}\:\:\mathrm{of}\:\mathrm{cyclohexanol} \\ $$
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