Question Number 164477 by mathocean1 last updated on 17/Jan/22 $${Using}\:{the}\:{definition},\:{show}\:{that}\: \\ $$$${U}_{{n}} =\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{{sin}\left({k}\right)}{{k}!}\:{is}\:{a}\:{sequence}\:{of}\:{Cauchy}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 164478 by mathocean1 last updated on 17/Jan/22 $${Given}\:\begin{cases}{{u}_{\mathrm{0}} =\alpha\:\in\:\mathbb{C}}\\{{u}_{{n}+\mathrm{1}} =\frac{{u}_{{n}} +\mid{u}_{{n}} \mid}{\mathrm{2}}}\end{cases}\:;\:{n}\in\:\mathbb{N} \\ $$$${where}\:\left({u}_{{n}} \right)\:_{{n}\in\mathbb{N}} \:{is}\:{a}\:{complex}\:{sequence}. \\ $$$${Determinate}\:{the}\:{sequence}\:\left({Im}\left({u}_{{n}} \right)\right)\:_{{n}\in\mathbb{N}} \\ $$$${and}\:{calculate}\:{its}\:{limit}. \\ $$$${NB}:\:{Im}\left({u}_{{n}}…
Question Number 164473 by mathocean1 last updated on 17/Jan/22 $${Show}\:{for}\:{z}_{\mathrm{1}} ;\:{z}_{\mathrm{2}\:} \:\in\:\mathbb{C}\:{that}: \\ $$$$\mid{z}_{\mathrm{1}} +{z}_{\mathrm{2}} \mid^{\mathrm{2}} +\mid{z}_{\mathrm{1}} −{z}_{\mathrm{2}} \mid^{\mathrm{2}} =\mathrm{2}\left(\mid{z}_{\mathrm{1}} \mid^{\mathrm{2}} +\mid{z}_{\mathrm{2}} \mid^{\mathrm{2}} \right). \\…
Question Number 164474 by mathocean1 last updated on 17/Jan/22 $${E}=\left\{{x}\:\in\:\mathbb{Q}_{+} :{x}^{\mathrm{2}} >\mathrm{3}\right\}.\: \\ $$$${Show}\:{that}\:{E}\:{has}\:{not}\:{lower}\:{bound} \\ $$$${in}\:\mathbb{Q}. \\ $$$$\left[{Montrez}\:{que}\:{E}\:{n}'{admet}\:{pas}\:{de}\:{borne}\right. \\ $$$$\left.{inferieure}\:{dans}\:\mathbb{Q}\right] \\ $$ Terms of Service…
Question Number 164475 by mathocean1 last updated on 17/Jan/22 $${Etudiez}\:\:{la}\:{convergence}\:{de}\:{de}\:{la} \\ $$$${suite}\:{U}_{{n}} =\frac{\mathrm{1}+{cos}\left({n}\right)+\mathrm{2}{n}}{{ni}+\sqrt{\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)}}\:;\:{n}\:\in\:\mathbb{N}. \\ $$$$\left[{study}\:{the}\:{convergence}\:{of}\:{U}_{{n}} \right] \\ $$ Answered by puissant last updated on 19/Jan/22…
Question Number 164471 by SANOGO last updated on 17/Jan/22 $$\:{une}\:{primitive}\:{de}\:{ln}\left(\mathrm{1}−{x}^{\mathrm{2}} \right){dx} \\ $$$${puis}\:{la}\:{convergence}\:{de}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}−{x}^{\mathrm{2}} \right){dx} \\ $$ Answered by Ar Brandon last updated on…
Question Number 98913 by mr W last updated on 17/Jun/20 $${solve} \\ $$$${f}\:'\left({x}\right)={f}\left({f}\left({x}\right)\right) \\ $$ Commented by john santu last updated on 17/Jun/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{Kx}^{\beta} \\…
Question Number 33363 by soufiane zarik last updated on 15/Apr/18 Commented by soufiane zarik last updated on 15/Apr/18 $$\mathrm{thank}\:\mathrm{you}\:\mathrm{sir}\:!! \\ $$ Commented by Rasheed.Sindhi last…
Question Number 33330 by artibunja last updated on 14/Apr/18 Answered by MJS last updated on 15/Apr/18 $$\mid\mathrm{3}^{\mathrm{tan}\:\pi{x}} −\frac{\mathrm{3}}{\mathrm{3}^{\mathrm{tan}\:\pi{x}} }\mid\geqslant\mathrm{2} \\ $$$$\mid\frac{\mathrm{3}^{\mathrm{2tan}\:\pi{x}} −\mathrm{3}}{\mathrm{3}^{\mathrm{tan}\:\pi{x}} }\mid\geqslant\mathrm{2} \\ $$$$\mid\mathrm{3}^{\mathrm{2tan}\:\pi{x}}…
Question Number 33317 by mondodotto@gmail.com last updated on 14/Apr/18 $$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{radius}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{circle}} \\ $$$$\boldsymbol{\mathrm{wich}}\:\boldsymbol{\mathrm{inscribes}}\:\boldsymbol{\mathrm{an}}\:\boldsymbol{\mathrm{equalateral}}\:\boldsymbol{\mathrm{triangle}} \\ $$$$\boldsymbol{\mathrm{with}}\:\boldsymbol{\mathrm{perimeter}}\:\boldsymbol{\mathrm{of}}\:\mathrm{24}\boldsymbol{\mathrm{cm}} \\ $$ Answered by MJS last updated on 14/Apr/18 $$\mathrm{I}'\mathrm{m}\:\mathrm{not}\:\mathrm{sure}\:\mathrm{if}\:\mathrm{you}\:\mathrm{mean}\:\mathrm{the} \\…