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Question Number 127553 by mathocean1 last updated on 30/Dec/20 $${f}\left({x}\right)=\sqrt{\frac{{x}^{\mathrm{3}} }{{x}−\mathrm{1}}} \\ $$$${calculate}: \\ $$$$\underset{{x}\rightarrow\mathrm{0}^{−} } {{lim}f}\left({x}\right)\:;\:\underset{{x}\rightarrow\mathrm{0}^{+} } {{lim}f}\left({x}\right);\:\underset{{x}\rightarrow\mathrm{1}^{−} } {{lim}f}\left({x}\right); \\ $$$$\underset{{x}\rightarrow\mathrm{1}^{+} } {{lim}f}\left({x}\right);\:\underset{{x}\rightarrow+\infty}…
Question Number 62016 by kiplangatryan89@gmail.com last updated on 14/Jun/19 $${the}\:\mathrm{2}\:{and}\:\mathrm{3}\:{term}\:{of}\:{GP}\:\:{is}\:\mathrm{24} \\ $$$${and}\:\mathrm{12}\left({x}+\mathrm{1}\right).{If}\:{the}\:{sum}\:{of}\:{the}\: \\ $$$${first}\:\mathrm{3}\:{terms}\:{is}\:\mathrm{76}.{Find}\:{the}\:{value} \\ $$$${of}\:{x} \\ $$ Commented by Tony Lin last updated on…
Question Number 62014 by Tawa1 last updated on 14/Jun/19 Answered by MJS last updated on 14/Jun/19 $$\mathrm{1} \\ $$$$\mathrm{5}×\mathrm{6}=\mathrm{30} \\ $$$$\mathrm{2} \\ $$$$\mathrm{4}×\mathrm{3}×\mathrm{2}=\mathrm{24} \\ $$…
Question Number 193087 by Abdullahrussell last updated on 03/Jun/23 Answered by Frix last updated on 03/Jun/23 $${x}^{\mathrm{4}} +\mathrm{2}{x}^{\mathrm{3}} −\mathrm{4}{x}−\mathrm{2} \\ $$$$\left({x}+\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{4}} −\frac{\mathrm{3}}{\mathrm{2}}\left({x}+\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} −\mathrm{3}\left({x}+\frac{\mathrm{1}}{\mathrm{2}}\right)−\frac{\mathrm{3}}{\mathrm{16}} \\ $$$$\left(\left({x}+\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}}…
Question Number 193080 by Mastermind last updated on 03/Jun/23 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{for}\:\mathrm{a},\mathrm{b}\in\mathbb{R}, \\ $$$$\mid\mathrm{a}−\mathrm{b}\mid\geqslant\mid\mathrm{a}\mid−\mid\mathrm{b}\mid \\ $$$$ \\ $$$$\left(\mathrm{Hint}:\:\mathrm{write}\:\mathrm{a}=\left(\mathrm{a}−\mathrm{b}\right)+\mathrm{b}\right. \\ $$ Answered by Subhi last updated on 03/Jun/23…
Question Number 127547 by Mathgreat last updated on 30/Dec/20 Answered by mr W last updated on 31/Dec/20 Commented by mr W last updated on 31/Dec/20…
Question Number 62010 by aliesam last updated on 13/Jun/19 $${if}\: \\ $$$$ \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} −\mathrm{2}{xyz}=\mathrm{1} \\ $$$${prove}\:{that} \\ $$$$ \\ $$$$\frac{{dx}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}\:+\:\frac{{dy}}{\:\sqrt{\mathrm{1}−{y}^{\mathrm{2}} }}\:+\:\frac{{dz}}{\:\sqrt{\mathrm{1}−{z}^{\mathrm{2}}…