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Question Number 200060 by sonukgindia last updated on 13/Nov/23 Answered by cortano12 last updated on 13/Nov/23 $$\:\mathrm{L}=\:\underset{{b}\rightarrow{a}} {\mathrm{lim}}\:\frac{\mathrm{2}{ab}−{a}\sqrt{{ab}}−{ab}}{\left({a}+\sqrt{{ab}}\right)\left({b}−{a}\right)} \\ $$$$\:\:=\:\underset{{b}\rightarrow{a}} {\mathrm{lim}}\:\frac{{ab}−{a}\sqrt{{ab}}}{\left({a}+\sqrt{{ab}}\right)\left({b}−{a}\right)} \\ $$$$\:=\:\underset{{b}\rightarrow{a}} {\mathrm{lim}}\:\frac{\sqrt{{ab}}\:\left(\sqrt{{ab}}−{a}\right)}{\left({a}+\sqrt{{ab}}\right)\left({b}−{a}\right)}\: \\…

Question Number 200075 by sonukgindia last updated on 13/Nov/23 Answered by ajfour last updated on 13/Nov/23 $${R}\mathrm{cos}\:\theta=\frac{{a}+{b}}{\mathrm{2}} \\ $$$${R}={b}\mathrm{cos}\:\theta \\ $$$$\Rightarrow\:\:\mathrm{2}{b}\mathrm{cos}\:^{\mathrm{2}} \theta={a}+{b} \\ $$$$\frac{{a}}{{b}}=\mathrm{2cos}\:^{\mathrm{2}} \theta−\mathrm{1}…

Question Number 200007 by Hummayoun last updated on 12/Nov/23 $${f}\left({x}\right)=\sqrt{{x}} \\ $$$${g}\left({x}\right)=\mathrm{2}{x}+\mathrm{1} \\ $$$${fog}\left({x}\right)={f}\left(\mathrm{2}{x}+\mathrm{1}\right) \\ $$$${fog}\left({x}\right)=\sqrt{\mathrm{2}{x}+\mathrm{1}} \\ $$$${gof}\left({x}\right)={g}\left(\sqrt{\left.{x}\right)}\right. \\ $$$${gof}\left({x}\right)=\mathrm{2}\sqrt{{x}} \\ $$ Terms of Service…

Question Number 199987 by Yakubu last updated on 11/Nov/23 $$\:\boldsymbol{{Use}}\:\boldsymbol{{mathematical}}\:\boldsymbol{{induction}} \\ $$$$\:\boldsymbol{{to}}\:\boldsymbol{{prove}}\:\boldsymbol{{that}}\:\boldsymbol{{the}}\:\boldsymbol{{statement}} \\ $$$$\:\boldsymbol{\mathrm{a}}+\left(\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{d}}\right)+\left(\boldsymbol{\mathrm{a}}+\mathrm{2}\boldsymbol{\mathrm{d}}\right)+…+\left(\boldsymbol{\mathrm{a}}+\left(\boldsymbol{\mathrm{n}}−\mathrm{1}\right)\boldsymbol{\mathrm{d}}\right)=\frac{\boldsymbol{\mathrm{n}}}{\mathrm{2}}\left[\mathrm{2}\boldsymbol{\mathrm{a}}+\left(\boldsymbol{\mathrm{n}}−\mathrm{1}\right)\boldsymbol{\mathrm{d}}\right] \\ $$$$\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{true}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{all}}\:\boldsymbol{\mathrm{natural}}\:\boldsymbol{\mathrm{numbers}} \\ $$$$\boldsymbol{\mathrm{A}{ny}}\:\boldsymbol{{help}}\:\boldsymbol{{please}} \\ $$ Answered by Rasheed.Sindhi last updated…

Question Number 199979 by Yakubu last updated on 11/Nov/23 $$ \\ $$Please help me out The following statements are true of inhabitants in Town A.…