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Question Number 205138 by Thokna last updated on 10/Mar/24 $${A}=\underset{{x}\rightarrow\mathrm{0}\:\:} {\mathrm{lim}}\frac{\mathrm{1}−\mathrm{cos2}{x}}{\mathrm{2}{x}^{\mathrm{2}} } \\ $$$$\:\:\:\:=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{2sin}^{\mathrm{2}} {x}}{\mathrm{2}{x}^{\mathrm{2}} } \\ $$$$\:\:\:\:=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{sin}{x}}{{x}}\right)^{\mathrm{2}} =\mathrm{1} \\ $$$${B}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}}{{x}\mathrm{cot}{x}} \\…
Question Number 205054 by SANOGO last updated on 06/Mar/24 $${prove} \\ $$$$\left({lim}\:{sup}\left({A}_{{n}} \right)\right)^{{c}} =\:{lim}\:{inf}\left({A}_{{n}} ^{{c}} \right) \\ $$ Commented by aleks041103 last updated on 11/Mar/24…
Question Number 205055 by SANOGO last updated on 06/Mar/24 $$\left({lim}\:{inf}\left({A}_{{n}} \right)\right)^{{c}} \:={limsup}\left({A}_{{n}} ^{{c}} \right)\:\:\:\:\:{prove} \\ $$ Answered by pi314 last updated on 09/Mar/24 $${What}\:{de}\:{you}\:{mean}\:{Withe}\:{A}_{{n}} \\…
Question Number 205001 by rajusasmal last updated on 05/Mar/24 Answered by TonyCWX08 last updated on 05/Mar/24 $$\mathrm{44}.\: \\ $$$${x}^{\mathrm{2}} −{y}^{\mathrm{2}} \\ $$$$=\left({asec}\left(\theta\right)+{btan}\left(\theta\right)\right)^{\mathrm{2}} −\left({atan}\left(\theta\right)+{bsec}\left(\theta\right)\right)^{\mathrm{2}} \\ $$$$={a}^{\mathrm{2}}…
Question Number 204978 by SANOGO last updated on 04/Mar/24 Answered by witcher3 last updated on 04/Mar/24 $$\mathrm{Soit}\:\mathrm{U}_{\mathrm{n}} ^{\mathrm{k}} \:\mathrm{une}\:\mathrm{suite}\:\mathrm{de}\:\mathrm{cauchy}\:\:\mathrm{Dans}\:\mathrm{C}_{\mathrm{0}} \\ $$$$\forall\mathrm{k}\:\:\mathrm{U}_{\mathrm{n}} ^{\mathrm{k}} \in\mathrm{C}_{} ^{\mathbb{N}} ;\underset{\mathrm{n}\rightarrow\infty}…
Question Number 204961 by naka3546 last updated on 04/Mar/24 $$\int\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{cot}\:\mathrm{3}{x}}\:{dx}\:=\:\: \\ $$ Answered by TonyCWX08 last updated on 04/Mar/24 $${let}\:{t}\:=\:\mathrm{3}{x} \\ $$$${dt}\:=\:\mathrm{3}\:{dx} \\ $$$$ \\…
Question Number 204963 by TonyCWX08 last updated on 04/Mar/24 $${x}^{\mathrm{2}} +{z}^{\mathrm{2}} ={y}^{\mathrm{2}} +{z}^{\mathrm{2}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 204948 by TonyCWX08 last updated on 03/Mar/24 $${prove}\: \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} +\sqrt[{\mathrm{3}}]{{abc}}\geqslant\mathrm{4} \\ $$$${if} \\ $$$${ab}+{bc}+{ac}=\mathrm{3} \\ $$ Commented by TonyCWX08 last…
Question Number 204957 by CrispyXYZ last updated on 03/Mar/24 $$\mathrm{2}×\mathrm{2}\:\mathrm{matrix}\:\boldsymbol{\mathrm{A}}\:\mathrm{and}\:\boldsymbol{\mathrm{B}}\:\mathrm{satisfy}\:\mathrm{that} \\ $$$$\boldsymbol{\mathrm{AB}}+\boldsymbol{\mathrm{A}}=\boldsymbol{\mathrm{BA}}+\boldsymbol{\mathrm{B}}. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\left(\boldsymbol{\mathrm{A}}−\boldsymbol{\mathrm{B}}\right)^{\mathrm{2}} =\boldsymbol{\mathrm{O}}. \\ $$ Answered by Rajpurohith last updated on 04/Mar/24 $${Need}\:{not}\:{hold}\:{true}!…