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AllQuestion and Answers: Page 1410
Question Number 60946 Answers: 3 Comments: 4
$$\mathrm{Find}\:\mathrm{x}:\:\:\:\:\:\:\mathrm{x}^{\mathrm{x}} \:\:=\:\:\mathrm{2x} \\ $$
Question Number 60944 Answers: 1 Comments: 1
$$\int\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\frac{\mathrm{3}}{\mathrm{2}}} } \\ $$$${solve}\:{this}\:{pls} \\ $$
Question Number 60938 Answers: 0 Comments: 1
$$\int\frac{{csc}^{\mathrm{2019}} \left({x}\right)}{{sec}^{\mathrm{5}} \left({x}\right)}\:{tan}^{\mathrm{2}} \left({x}\right)\:{dx} \\ $$
Question Number 60921 Answers: 1 Comments: 0
$${x}^{\mathrm{2}} \frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\:{x}\frac{{dy}}{{dx}}\:+\:{y}=\mathrm{0} \\ $$$${please}\:{solve}\:{this}\:{Euler}\:{equation} \\ $$
Question Number 60915 Answers: 0 Comments: 0
$${Let}\:\:{Fibonacci}\:\:{sequence}\:\:\left({F}_{{n}} \right)\:_{{n}\geqslant\mathrm{0}} \\ $$$${where}\:\:{F}_{\mathrm{0}} \:=\:\mathrm{0},\:{F}_{\mathrm{1}} \:=\:\mathrm{1},\:\:{and}\:\:{F}_{{n}+\mathrm{2}} \:\:=\:\:{F}_{{n}+\mathrm{1}} \:+\:{F}_{{n}} \:\:\:\:,\:\:\forall\:{n}\:\:\geqslant\:\:\mathrm{0}\:. \\ $$$${Find}\:\:{the}\:\:{least}\:\:{of}\:\:{natural}\:\:{numbers}\:\:{n}\:\:{so}\:\:{that} \\ $$$${F}_{{n}} \:\:\:{and}\:\:\:{F}_{{n}+\mathrm{1}} \:−\:\mathrm{1}\:\:\:{can}\:\:{be}\:\:{divided}\:\:{by}\:\:\:{F}_{\mathrm{2019}} \:. \\ $$
Question Number 60906 Answers: 0 Comments: 1
Question Number 60905 Answers: 3 Comments: 0
$${if}\:{x}+\frac{\mathrm{1}}{{x}}=\sqrt{\mathrm{3}}.{find} \\ $$$${x}^{\mathrm{24}} +{x}^{\mathrm{18}} +{x}^{\mathrm{6}} +\mathrm{1} \\ $$
Question Number 60901 Answers: 1 Comments: 0
$${find}\:\int\:\:{arctan}\left(\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} }\right){dx}\: \\ $$
Question Number 60894 Answers: 0 Comments: 0
$${study}\:{the}\:{convergence}\:{of}\: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\sqrt{\mathrm{1}+\mathrm{2}{x}}−\sqrt{\mathrm{1}+{x}}}{{ln}\left(\mathrm{1}+{x}\right)}{dx}\:\:{and}\:{determine}\:{its} \\ $$$${value}. \\ $$
Question Number 60893 Answers: 1 Comments: 1
$${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{dx}}{\sqrt{\mathrm{2}}{cos}^{\mathrm{2}} {x}\:+\sqrt{\mathrm{3}}{sin}^{\mathrm{2}} {x}} \\ $$
Question Number 60910 Answers: 1 Comments: 7
Question Number 60888 Answers: 1 Comments: 1
Question Number 60873 Answers: 2 Comments: 5
Question Number 60881 Answers: 0 Comments: 3
$$\underset{−\pi} {\overset{\pi} {\int}}{sin}\left(\frac{\mathrm{1}}{\mathrm{1}−{x}^{\mathrm{2}} }\right)\:{dx} \\ $$
Question Number 60862 Answers: 0 Comments: 0
Question Number 60854 Answers: 2 Comments: 4
$$\left({x}^{\mathrm{4}} −\mathrm{3}{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{1}\right)/\left({x}−\mathrm{1}\right) \\ $$$$ \\ $$$$ \\ $$
Question Number 60853 Answers: 2 Comments: 0
$$\sqrt{\mathrm{5}−\mathrm{12}{i}}+\sqrt{\mathrm{5}+\mathrm{12}{i}}=? \\ $$
Question Number 60849 Answers: 1 Comments: 5
$${For}\:{all}\:\theta\:{in}\:\left[\mathrm{0},\:\pi/\mathrm{2}\right]\:{show}\:{that}\:{cos}\left({sin}\theta\right)\geqslant{sin}\left({cos}\theta\right). \\ $$
Question Number 61612 Answers: 0 Comments: 7
Question Number 60817 Answers: 4 Comments: 2
$$\boldsymbol{\mathrm{V}}=\frac{\mathrm{4}}{\mathrm{3}}\boldsymbol{\pi\mathrm{R}}^{\mathrm{3}} \:\:\:\boldsymbol{\mathrm{prove}} \\ $$
Question Number 60816 Answers: 1 Comments: 0
$$\boldsymbol{\mathrm{S}}=\mathrm{4}\boldsymbol{\pi\mathrm{R}}^{\mathrm{2}} \:\:\:\boldsymbol{\mathrm{prove}} \\ $$
Question Number 60814 Answers: 1 Comments: 0
$${find}\:{x}\:{given}\:{that} \\ $$$$\mathrm{9}^{{sin}^{\mathrm{2}} {x}} +\mathrm{9}^{{cos}^{\mathrm{2}} {x}} =\mathrm{2}\: \\ $$$$ \\ $$
Question Number 60812 Answers: 0 Comments: 5
Question Number 60797 Answers: 0 Comments: 2
$$\int\frac{{e}^{{w}} }{{w}^{{n}+\mathrm{1}} }{dw},\:{n}\in\mathbb{N} \\ $$
Question Number 60791 Answers: 1 Comments: 2
$$\int\frac{{e}^{{n}} }{{x}^{{n}+\mathrm{1}} }{dx},\:\mathrm{n}\in\mathbb{N} \\ $$
Question Number 60788 Answers: 2 Comments: 1
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