Question Number 106019 by ZiYangLee last updated on 02/Aug/20 Answered by ajfour last updated on 02/Aug/20 $$\frac{\mathrm{3}}{{a}+{b}+{c}}−\frac{{a}+\left({a}+{b}+{c}\right)}{\left({a}+{b}\right)\left({a}+{c}\right)}=\mathrm{0} \\ $$$$\Rightarrow\:\mathrm{3}\left({a}+{b}\right)\left({a}+{c}\right)−{a}\left({a}+{b}+{c}\right) \\ $$$$\:\:\:\:\:\:−\left({a}+{b}+{c}\right)^{\mathrm{2}} =\mathrm{0} \\ $$$${a}^{\mathrm{2}} +{bc}−{b}^{\mathrm{2}}…
Question Number 171552 by 0731619 last updated on 17/Jun/22 Answered by alephzero last updated on 17/Jun/22 $$\mathrm{1}−{x}^{\mathrm{3}} \:\sim\:−{x}^{\mathrm{3}} \\ $$$$\sqrt[{\mathrm{3}}]{−{x}^{\mathrm{3}} }\:=\:−\sqrt[{\mathrm{3}}]{{x}^{\mathrm{3}} }\:=\:−{x} \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}{x}+\left(−{x}\right)\:=\:\mathrm{0}…
Question Number 40474 by KMA last updated on 22/Jul/18 $${When}\:{x}^{\mathrm{7}} −\mathrm{97}{x}^{\mathrm{6}} −\mathrm{199}{x}^{\mathrm{5}} +\mathrm{99}{x}^{\mathrm{4}} − \\ $$$$\mathrm{2}{x}+\mathrm{190}\:{is}\:{divided}\:{by}\:{x}−\mathrm{99}\:{find}\: \\ $$$${the}\:{remainder}. \\ $$ Answered by $@ty@m last updated…
Question Number 106005 by bemath last updated on 02/Aug/20 $$\left(\mathrm{1}\right)\:\mathrm{y}'\:=\:\frac{\mathrm{y}−\mathrm{2x}}{\mathrm{2y}+\mathrm{x}} \\ $$$$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2}^{\mathrm{x}} −\mathrm{cos}\:\mathrm{x}}{\mathrm{sin}\:\mathrm{x}} \\ $$ Answered by bobhans last updated on 02/Aug/20 $$\left(\mathrm{1}\right)\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{y}−\mathrm{2x}}{\mathrm{2y}+\mathrm{x}}\:\:\left[\:\mathrm{set}\:\mathrm{y}\:=\:\flat\mathrm{x}\:\right]\: \\…
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Question Number 171514 by mokys last updated on 16/Jun/22 $$\:{compute}\:{by}\:{betta}\:{function}\:\int_{\mathrm{0}} ^{\:\mathrm{4}\pi} \sqrt{{cscx}}\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 40434 by vitlu last updated on 21/Jul/18 $${prove}\:{that}\:\mathrm{ln}\left({x}\right)\:{is}\:{irrational}\:{for}\:{x}\:{natural} \\ $$ Commented by math khazana by abdo last updated on 21/Jul/18 $${let}\:{x}={n}\:{natural}\:>\mathrm{1}\:{let}\:{prove}\:{that}\:{ln}\left({n}\right)\notin{Q} \\ $$$${if}\:{ln}\left({n}\right)\in{Q}\:\:\exists\left({p},{q}\right)\in{N}^{\mathrm{2}}…
Question Number 171497 by MathsFan last updated on 16/Jun/22 Commented by MathsFan last updated on 16/Jun/22 $${Any}\:{help}\:{please} \\ $$ Commented by cortano1 last updated on…
Question Number 171499 by MathsFan last updated on 16/Jun/22 $$\boldsymbol{\mathrm{The}}\:\boldsymbol{\mathrm{sum}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{sample}}\:\boldsymbol{\mathrm{of}}\:\mathrm{20}\:\boldsymbol{\mathrm{numbers}}\:\boldsymbol{\mathrm{is}} \\ $$$$\mathrm{320}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{sum}}\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{their}}\:\boldsymbol{\mathrm{squares}}\: \\ $$$$\:\boldsymbol{\mathrm{is}}\:\mathrm{5840}.\:\boldsymbol{\mathrm{Calculate}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{mean}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\: \\ $$$$\:\boldsymbol{\mathrm{first}}\:\boldsymbol{\mathrm{nineteen}}\:\boldsymbol{\mathrm{numbers}}\:\boldsymbol{\mathrm{if}}\:\boldsymbol{\mathrm{the}}\:\mathrm{20}^{\boldsymbol{\mathrm{th}}} \: \\ $$$$\boldsymbol{\mathrm{observation}}\:\boldsymbol{\mathrm{is}}\:\mathrm{25}. \\ $$ Answered by Rasheed.Sindhi last…
Question Number 105949 by bachamohamed last updated on 01/Aug/20 $$\int\boldsymbol{{arctan}}\left(\left(\boldsymbol{{t}}^{\mathrm{2}} −\mathrm{1}\right)\sqrt{\boldsymbol{\beta}}\right)\boldsymbol{{dt}}=? \\ $$ Answered by Her_Majesty last updated on 01/Aug/20 $$\mathrm{1}^{{st}} \:{step}\:{by}\:{parts} \\ $$$$\Rightarrow \\…