Question Number 67057 by Tony Lin last updated on 22/Aug/19 $$\left(\mathrm{1}\right){find}\:\cap_{{n}=\mathrm{1}} ^{\infty} \left[\mathrm{0},\:\frac{\mathrm{1}}{{n}}\right) \\ $$$$\left(\mathrm{2}\right){find}\:\cup_{{n}=\mathrm{2}} ^{\infty} \left[\frac{\mathrm{1}}{{n}},\:\mathrm{1}−\frac{\mathrm{1}}{{n}}\right] \\ $$ Answered by Kunal12588 last updated on…
Question Number 67034 by mathmax by abdo last updated on 22/Aug/19 $${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{{cos}\left(\mathrm{2}{nx}\right)}{{n}} \\ $$ Commented by mathmax by abdo last updated on 23/Aug/19…
Question Number 132574 by liberty last updated on 15/Feb/21 $$\mathrm{Given}\:\mathrm{f}\left(\mathrm{x}\right)=\:\mathrm{log}\:_{\mathrm{2020}} \left(\mathrm{x}\right)\:\mathrm{and}\: \\ $$$$\mathrm{p}^{\left(\mathrm{p}\right)^{\mathrm{p}^{\mathrm{2020}} } } \:=\:\mathrm{2020}\:\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{f}\left(\mathrm{p}\right)\:=\:… \\ $$$$\left(\mathrm{a}\right)\sqrt[{\mathrm{2020}}]{\mathrm{2020}}\:\:\:\:\:\left(\mathrm{c}\right)\:\sqrt[{\mathrm{2020}}]{\frac{\mathrm{1}}{\mathrm{2020}}} \\ $$$$\left(\mathrm{b}\right)\:\frac{\mathrm{1}}{\mathrm{2020}}\:\:\:\:\:\:\:\:\:\left(\mathrm{d}\right)\:\mathrm{2020}\:\:\:\:\:\:\left(\mathrm{e}\right)\:\mathrm{log}\:_{\mathrm{10}} \left(\mathrm{2020}\right) \\ $$…
Question Number 67023 by mathmax by abdo last updated on 21/Aug/19 $${find}\:{the}\:{sequence}\:{U}_{{n}} \:{wich}\:{verify}\:\:{U}_{{n}} +{U}_{{n}+\mathrm{1}} ={sin}\left({n}\right)\:\:\forall{n}\:{from}\:{n} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 67014 by mathmax by abdo last updated on 21/Aug/19 $${solve}\:{y}^{''} +{x}^{\mathrm{2}} {y}^{'} ={e}^{−{x}} {sin}\left(\mathrm{3}{x}\right) \\ $$ Commented by mathmax by abdo last updated…
Question Number 67015 by mathmax by abdo last updated on 21/Aug/19 $${let}\:{f}\left({x}\right)\:={arctan}\left(\mathrm{1}+{e}^{−\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }} \right) \\ $$$${calculate}\:{f}^{'} \left({x}\right)\:\:{and}\:{f}^{''} \left({x}\right). \\ $$$$\left.\mathrm{1}\right){find}\:{lim}_{{x}\rightarrow+\infty} {f}\left({x}\right)\:{and}\:{lim}_{{x}\rightarrow−\infty} \:\:\:{f}\left({x}\right) \\ $$$$\left.\mathrm{3}\right){study}\:{the}\:{variation}\:{of}\:{f}\left({x}\right) \\…
Question Number 67010 by mathmax by abdo last updated on 21/Aug/19 $${calculate}\:\:\sum_{{n}=\mathrm{4}} ^{+\infty} \:\:\:\:\frac{{n}}{\left({n}^{\mathrm{2}} −\mathrm{9}\right)^{\mathrm{2}} } \\ $$ Commented by mathmax by abdo last updated…
Question Number 67013 by mathmax by abdo last updated on 21/Aug/19 $${find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{\left({n}+\mathrm{1}\right){n}^{\mathrm{3}} } \\ $$ Commented by mathmax by abdo last updated…
Question Number 132496 by mathmax by abdo last updated on 14/Feb/21 $$\mathrm{calculateA}_{\mathrm{n}} =\:\sum_{\mathrm{n}=\mathrm{1}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{n}^{\mathrm{2}} }\mathrm{cos}\left(\mathrm{n}\right)\:\mathrm{andB}_{\mathrm{n}} =\:\sum_{\mathrm{n}=\mathrm{1}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{n}^{\mathrm{2}} }\mathrm{cos}\left(\frac{\mathrm{n}\pi}{\mathrm{3}}\right) \\ $$ Answered…
Question Number 66937 by Cmr 237 last updated on 20/Aug/19 Answered by mr W last updated on 21/Aug/19 $${let}\:{t}=\mathrm{81}^{\mathrm{sin}^{\mathrm{2}} \:{x}} \\ $$$$\mathrm{81}^{\mathrm{cos}^{\mathrm{2}} \:{x}} =\mathrm{81}^{\mathrm{1}−\mathrm{sin}^{\mathrm{2}} \:{x}}…