Question Number 83020 by mathmax by abdo last updated on 27/Feb/20 $${find}\:{the}\:{sequence}\:{u}_{{n}} \:{wich}\:{verify}\:{u}_{{n}} +{u}_{{n}+\mathrm{1}} =\frac{{sin}\left({n}\right)}{{n}}\:\:\forall{n}>\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 83021 by mathmax by abdo last updated on 27/Feb/20 $${find}\:{the}\:{sequence}\:{v}_{{n}} \:{wich}\:{verify}\:{v}_{{n}} +{v}_{{n}+\mathrm{1}} =\frac{\left(−\mathrm{1}\right)^{{n}} }{\:\sqrt{{n}}}\:\:\left({n}\geqslant\mathrm{1}\right) \\ $$$${is}\:\left({v}_{{n}} \right)\:{convergente}? \\ $$ Terms of Service Privacy…
Question Number 83019 by mathmax by abdo last updated on 27/Feb/20 $${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\frac{\mathrm{1}−\sqrt{\mathrm{1}+{x}+{x}^{\mathrm{2}} }{cos}\left(\mathrm{2}{x}\right)}{{x}^{\mathrm{3}} } \\ $$ Commented by mathmax by abdo last updated on…
Question Number 82973 by mathmax by abdo last updated on 26/Feb/20 $${calculate}\:{lim}_{{n}\rightarrow+\infty} \:\:\:\int_{\mathrm{0}} ^{{n}} \left(\mathrm{1}−\frac{{x}}{{n}}\right)^{{n}} {arctan}\left({nx}\right){dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 148501 by mathmax by abdo last updated on 28/Jul/21 $$\mathrm{let}\:\mathrm{U}_{\mathrm{n}} =\left\{\mathrm{z}\in\mathrm{C}\:/\mathrm{z}^{\mathrm{n}} \:=\mathrm{1}\right\}\:\:\mathrm{simplify} \\ $$$$\sum_{\mathrm{p}=\mathrm{0}} ^{\mathrm{2n}−\mathrm{1}} \:\mathrm{w}^{\mathrm{p}} \:\:\:\:\:\:\:\:\mathrm{with}\:\mathrm{w}\in\mathrm{U}_{\mathrm{n}} \:\:\: \\ $$$$\mathrm{and}\:\:\sum_{\mathrm{p}=\mathrm{0}} ^{\mathrm{2n}−\mathrm{1}} \left(\mathrm{2w}\:+\mathrm{1}\right)^{\mathrm{p}} \\…
Question Number 148498 by mathmax by abdo last updated on 28/Jul/21 $$\mathrm{find}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{arctan}\left(\mathrm{2x}\right)}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx} \\ $$ Answered by mathmax by abdo last updated on…
Question Number 148502 by mathmax by abdo last updated on 28/Jul/21 $$\mathrm{let}\:\alpha\:\mathrm{and}\:\beta\:\mathrm{roots}\:\mathrm{of}\:\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{2} \\ $$$$\mathrm{simplify}\:\:\sum_{\mathrm{k}=\mathrm{0}} ^{\mathrm{n}−\mathrm{1}} \:\:\left(\alpha^{\mathrm{k}} \:+\beta^{\mathrm{k}} \right)\:\:\mathrm{and}\:\sum_{\mathrm{k}=\mathrm{0}} ^{\mathrm{n}−\mathrm{1}} \left(\:\frac{\mathrm{1}}{\alpha^{\mathrm{k}} }+\frac{\mathrm{1}}{\beta^{\mathrm{k}} }\right) \\ $$…
Question Number 82920 by abdomathmax last updated on 25/Feb/20 $${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \frac{{ln}\left(\mathrm{1}+{ln}\left(\mathrm{1}+{x}\right)\right)}{{x}} \\ $$ Answered by mind is power last updated on 25/Feb/20 $${ln}\left(\mathrm{1}+{x}\right)\sim{x} \\ $$$$\Rightarrow{ln}\left(\mathrm{1}+{ln}\left(\mathrm{1}+{x}\right)\right)\sim{ln}\left(\mathrm{1}+{x}\right)…
Question Number 17359 by ajfour last updated on 04/Jul/17 $$\mathrm{For}\:\mathrm{what}\:\mathrm{values}\:\mathrm{of}\:\mathrm{m},\:\mathrm{the}\:\mathrm{equation} \\ $$$$\left(\mathrm{1}+\mathrm{m}\right)\mathrm{x}^{\mathrm{2}} −\mathrm{2}\left(\mathrm{1}+\mathrm{3m}\right)\mathrm{x}+\left(\mathrm{1}+\mathrm{8m}\right)=\mathrm{0}\:; \\ $$$$\:\:\:\mathrm{m}\:\in\:\mathrm{R}\:,\:\mathrm{has}\:\mathrm{both}\:\mathrm{roots}\:\mathrm{positive}\:? \\ $$ Commented by ajfour last updated on 04/Jul/17 $$\mathrm{book}'\mathrm{s}\:\mathrm{answer}:…
Question Number 17354 by ajfour last updated on 04/Jul/17 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}\:: \\ $$$$\mid\mathrm{x}−\mathrm{1}\mid−\mid\mathrm{x}−\mathrm{2}\mid+\mid\mathrm{x}+\mathrm{1}\mid>\mid\mathrm{x}+\mathrm{2}\mid+\mid\mathrm{x}\mid−\mathrm{3}\:. \\ $$ Commented by ajfour last updated on 04/Jul/17 $$\mathrm{my}\:\mathrm{answer}:\:\mathrm{x}\in\:\left(−\mathrm{3},\:\mathrm{3}\right)−\left\{−\mathrm{1},\:\mathrm{1}\:\right\} \\ $$$$\mathrm{answer}\:\mathrm{in}\:\mathrm{book}:\:\:\mathrm{x}\in\:\left(\mathrm{1},\:\mathrm{3}\right)\:. \\…