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Category: Algebra

Question-136283

Question Number 136283 by JulioCesar last updated on 20/Mar/21 Answered by Ar Brandon last updated on 20/Mar/21 $$\int\mathrm{e}^{\mathrm{g}\left(\mathrm{x}\right)} \left[\mathrm{f}\left(\mathrm{x}\right)\mathrm{g}'\left(\mathrm{x}\right)+\mathrm{f}\:'\left(\mathrm{x}\right)\right]\mathrm{dx}=\mathrm{e}^{\mathrm{g}\left(\mathrm{x}\right)} \mathrm{f}\left(\mathrm{x}\right) \\ $$ Terms of Service…

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Question Number 5203 by FilupSmith last updated on 30/Apr/16 $$\mathrm{Silly}\:\mathrm{question} \\ $$$$ \\ $$$$\frac{\mathrm{1}}{\:\sqrt{\frac{{a}}{{b}}}}×\frac{\mathrm{1}}{{b}} \\ $$$$ \\ $$$$\mathrm{Does}\:\mathrm{this}\:\mathrm{equal}: \\ $$$$\frac{\mathrm{1}}{{b}\sqrt{\frac{{a}}{{b}}}}=\frac{\mathrm{1}}{\:\sqrt{{b}^{\mathrm{2}} \frac{{a}}{{b}}}}=\frac{\mathrm{1}}{\:\sqrt{{ab}}}\:???? \\ $$$$ \\ $$$$\mathrm{Ive}\:\mathrm{never}\:\mathrm{done}\:\mathrm{this}\:\mathrm{so}\:\mathrm{it}\:\mathrm{has}\:\mathrm{oddly}\:\mathrm{surprised}\:\mathrm{me}…

Question-5119

Question Number 5119 by sanusihammed last updated on 14/Apr/16 Commented by 123456 last updated on 15/Apr/16 $${x}=\sqrt{\mathrm{3}+\mathrm{2}\sqrt{\mathrm{2}}} \\ $$$${x}^{\mathrm{2}} =\mathrm{3}+\mathrm{2}\sqrt{\mathrm{2}} \\ $$$${x}=\sqrt{{a}}+\sqrt{{b}}\wedge{a}>\mathrm{0}\wedge{b}>\mathrm{0} \\ $$$${x}^{\mathrm{2}} ={a}+{b}+\mathrm{2}\sqrt{{ab}}…

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Question Number 5113 by FilupSmith last updated on 14/Apr/16 $$\mathrm{How}\:\mathrm{do}\:\mathrm{you}\:\mathrm{find}\:\mathrm{the}: \\ $$$$\left(\mathrm{1}\right)\:\:\mathrm{Focal}\:\mathrm{point} \\ $$$$\left(\mathrm{2}\right)\:\:\mathrm{Directrix} \\ $$$$\mathrm{for}\:{y}={ax}^{\mathrm{2}} +{bx}+{c} \\ $$$$ \\ $$$$\mathrm{For}\:\mathrm{simplicity},\:\mathrm{lets}\:\mathrm{assume}\:\mathrm{it}\:\mathrm{goes}\:\mathrm{throigh} \\ $$$$\mathrm{point}\:\left(\mathrm{0},\:\mathrm{0}\right). \\ $$…

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Question Number 5091 by FilupSmith last updated on 11/Apr/16 $$\mathrm{Part}\:\mathrm{1} \\ $$$${S}=\mathrm{ln}\left({a}+{bi}\right),\:\:\:\:\:\:{a},\:{b}\in\mathbb{R} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{i}^{\mathrm{2}} =−\mathrm{1} \\ $$$$\mathrm{is}\:{S}\in\mathbb{C}?\:\:\:\:\:\:\:\left({b}\neq\mathrm{0}\right) \\ $$$$ \\ $$$$\mathrm{Part}\:\mathrm{2} \\ $$$${t}=\mathrm{ln}\left(\mathrm{ln}\left(…\left(\mathrm{ln}\left({k}\right)\right)\right)\right),\:\:\:\:{k}\in\mathbb{R},\:{k}>\mathrm{1} \\ $$$$\therefore{t}\in\mathbb{C}?…