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Question Number 74886 Answers: 0 Comments: 1
$${calculate}\:\int\:\:\frac{{x}+\mathrm{1}}{\left({x}^{\mathrm{3}} +{x}−\mathrm{2}\right)^{\mathrm{2}} }{dx} \\ $$
Question Number 74885 Answers: 1 Comments: 0
$${calcilate}\:\sum_{{n}=\mathrm{1}} ^{\mathrm{16}} \:\frac{\mathrm{1}}{{n}^{\mathrm{3}} } \\ $$
Question Number 74884 Answers: 0 Comments: 2
$${calculate}\:\sum_{{n}=\mathrm{1}} ^{\mathrm{20}} \:\frac{\mathrm{1}}{{n}^{\mathrm{2}} } \\ $$$$ \\ $$
Question Number 74882 Answers: 1 Comments: 3
Question Number 74880 Answers: 1 Comments: 0
$${solve}\:{inR} \\ $$$$\sqrt[{\mathrm{5}}]{\mid{x}+\mathrm{1}\mid}−\sqrt[{\mathrm{10}}]{{x}^{\mathrm{2}} +\mathrm{4}{x}−\mathrm{9}}=\left(\mathrm{2}{x}−\mathrm{10}\right)\sqrt{{x}^{\mathrm{2}} +\mathrm{1}} \\ $$
Question Number 74870 Answers: 1 Comments: 1
$$\mathrm{solve}\:\mathrm{with}\:\mathrm{explanation} \\ $$$$\mathrm{li}\underset{\mathrm{x}\rightarrow\mathrm{0}^{−} } {\mathrm{m}}\left[\frac{\mathrm{x}}{\mathrm{sinx}}\right],\:\mathrm{where}\:\left[\:\:\right]\:\mathrm{represents}\:\mathrm{greatest}\:\mathrm{integer} \\ $$
Question Number 74863 Answers: 2 Comments: 1
Question Number 76203 Answers: 0 Comments: 7
Question Number 74861 Answers: 1 Comments: 0
Question Number 74860 Answers: 1 Comments: 0
Question Number 74853 Answers: 0 Comments: 2
$$\mathrm{Is}\:\mathrm{it}\:\mathrm{possible}\:\mathrm{to}\:\mathrm{combine}\:\mathrm{2}{cos}\left(\mathrm{90}°{x}\right)+{cos}\left(\mathrm{180}°{x}\right) \\ $$$$\mathrm{into}\:\mathrm{a}\:\mathrm{form}\:\mathrm{of}\:\:{a}\centerdot{cos}\left({b}\centerdot{x}+{c}\right) \\ $$$$\mathrm{2}{cos}\left(\frac{\pi}{\mathrm{2}}{x}\right)+{cos}\left(\pi{x}\right)\overset{?} {=}{a}\centerdot{cos}\left({bx}+{c}\right) \\ $$
Question Number 74840 Answers: 0 Comments: 3
Question Number 74825 Answers: 0 Comments: 5
Question Number 74821 Answers: 1 Comments: 0
Question Number 74819 Answers: 1 Comments: 2
$$\mathrm{Expand}\:\Sigma \\ $$$$\frac{\mathrm{4}{n}−\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{2}}{\mathrm{3}}\underset{{k}=\mathrm{1}} {\overset{{n}−\mathrm{1}} {\sum}}{cos}\left(\mathrm{120}{k}\right) \\ $$
Question Number 74817 Answers: 1 Comments: 0
Question Number 74802 Answers: 1 Comments: 4
Question Number 74801 Answers: 2 Comments: 2
$$\begin{cases}{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{y}}^{\mathrm{3}} =\mathrm{23}}\\{\boldsymbol{\mathrm{x}}^{\mathrm{3}} +\boldsymbol{\mathrm{y}}^{\mathrm{2}} =\mathrm{32}}\end{cases}\:\:\:\:\:\:\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{y}}\:. \\ $$
Question Number 74800 Answers: 1 Comments: 0
$${study}\:{the}\:{existence}\:{of}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{tcos}\left({tx}\right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt} \\ $$
Question Number 74799 Answers: 1 Comments: 0
$${prove}\:{that}\:\mathrm{0}\leqslant\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{t}^{\mathrm{2}} \:{e}^{−{nt}} }{{e}^{{t}} −\mathrm{1}}{dt}\:\leqslant\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\:\:{for}\:{n}\:{integr}\:{not}\:\mathrm{0} \\ $$
Question Number 74798 Answers: 0 Comments: 0
$${calculate}\:\int_{\mathrm{0}} ^{\pi} {ln}\left(\mathrm{1}−\mathrm{2}{xcos}\theta\:+{x}^{\mathrm{2}} \right){d}\theta\:\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$
Question Number 74797 Answers: 0 Comments: 0
$${find}\:{nsture}\:{of}\:{the}\:{serie}\:\Sigma\:{sin}\left(\pi{en}!\right) \\ $$
Question Number 74796 Answers: 0 Comments: 0
$${let}\:{U}_{{n}} =\left(−\mathrm{1}\right)^{{n}} \left\{{arcsin}\left(\frac{\mathrm{1}}{{n}}\right)−\frac{\mathrm{1}}{{n}}\right\}^{\frac{\mathrm{1}}{\mathrm{3}}} \\ $$$${study}\:{the}\:{convergence}\:{of}\:\Sigma\:{U}_{{n}} \\ $$
Question Number 74795 Answers: 1 Comments: 1
$${study}\:{the}\:{convergence}\:{of}\:\Sigma\:\frac{\mathrm{1}}{{nH}_{{n}} } \\ $$$${with}\:{H}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{k}} \\ $$
Question Number 74794 Answers: 0 Comments: 2
$${let}\:{A}\:=\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\:\:\:\mathrm{2}}\\{−\mathrm{1}\:\:\:\:\:\:\:\:\mathrm{1}}\end{pmatrix} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}^{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\:{e}^{{A}} \:{and}\:{e}^{−{A}} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\:{cosA}\:{and}\:{sinA} \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\:{ch}\left({A}\right)\:{and}\:{sh}\left({A}\right) \\ $$
Question Number 74790 Answers: 0 Comments: 0
$$\mathrm{4}{x}^{\mathrm{4}} +\mathrm{12}{x}\mathrm{3}+\mathrm{25}{x}\mathrm{2}{t}+\mathrm{24}{x}+\mathrm{16}\:{find}\:{the}\:{square}\:{root} \\ $$
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