Question Number 112501 by I want to learn more last updated on 08/Sep/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{convergent}\:\mathrm{of}\:\mathrm{the}\:\mathrm{power}\:\mathrm{series}:\:\:\:\underset{\mathrm{n}\:\:=\:\:\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{n}\:\:+\:\:\mathrm{2}}{\mathrm{n}}\right)^{\mathrm{n}^{\mathrm{2}} } \mathrm{x}^{\mathrm{n}} \\ $$ Terms of Service Privacy Policy…
Question Number 112497 by bemath last updated on 08/Sep/20 $$\mathrm{If}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\mathrm{2x}\:+\:\mathrm{asin}\:\mathrm{x}}{\mathrm{x}^{\mathrm{3}} }\:\mathrm{exist}\: \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{a}\:\mathrm{and}\:\mathrm{the}\:\mathrm{limit}? \\ $$ Answered by mathmax by abdo last updated on 08/Sep/20…
Question Number 112455 by john santu last updated on 08/Sep/20 $$\left(\mathrm{1}\right)\underset{{x}\rightarrow\mathrm{p}} {\mathrm{lim}}\:\frac{\mathrm{p}^{\mathrm{x}} −\mathrm{x}^{\mathrm{p}} }{\mathrm{x}^{\mathrm{x}} −\mathrm{p}^{\mathrm{p}} }\:?\: \\ $$$$\left(\mathrm{2}\right)\:{There}\:{are}\:\mathrm{4}\:{identical}\:{math}\:{books}, \\ $$$$\mathrm{2}\:{identical}\:{physics}\:{books}\:{and}\:\mathrm{2}\:{identical} \\ $$$${chemistry}\:{books}.\:{How}\:{many}\:{ways}\:{to} \\ $$$${compile}\:{the}\:{eight}\:{books}\:{on}\:{the}\: \\…
Question Number 112370 by Eric002 last updated on 07/Sep/20 $$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\frac{{x}−\lfloor{x}\rfloor}{{x}^{\mathrm{2}} } \\ $$$$\lfloor{x}\rfloor\:{is}\:{floor}\:{function} \\ $$ Commented by kaivan.ahmadi last updated on 07/Sep/20 $$\lfloor\mathrm{0}^{+}…
Question Number 112311 by bemath last updated on 07/Sep/20 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\sqrt{\frac{\mathrm{3sin}\:^{\mathrm{2}} \mathrm{x}+\mathrm{cos}\:\mathrm{2x}−\mathrm{1}}{\mathrm{x}.\mathrm{tan}\:\mathrm{2x}}}\:? \\ $$ Commented by Dwaipayan Shikari last updated on 07/Sep/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\sqrt{\frac{\mathrm{3}{sin}^{\mathrm{2}} {x}+\mathrm{1}−\mathrm{2}{sin}^{\mathrm{2}}…
Question Number 112273 by bemath last updated on 07/Sep/20 $$\:\left(\mathrm{1}\right)\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{e}^{\mathrm{x}} +\mathrm{e}^{−\mathrm{x}} \right)^{\frac{\mathrm{2}}{\mathrm{x}}} \:=? \\ $$$$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\left(\mathrm{cos}\:\mathrm{x}\right)^{−\mathrm{x}+\frac{\pi}{\mathrm{2}}} ? \\ $$$$\left(\mathrm{3}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\sqrt{\frac{\mathrm{1}+\mathrm{tan}\:\mathrm{x}}{\mathrm{x}^{\mathrm{2}} }}−\sqrt{\frac{\mathrm{1}−\mathrm{sin}\:\mathrm{x}}{\mathrm{x}^{\mathrm{2}} }\:}? \\ $$…
Question Number 46563 by Necxx last updated on 28/Oct/18 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{{a}^{{x}} +{b}^{{x}} +{c}^{{x}} }{\mathrm{3}}\right)^{\mathrm{1}/{x}} \\ $$ Answered by ajfour last updated on 28/Oct/18 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\mathrm{1}+\frac{{a}^{{x}}…
Question Number 112083 by bemath last updated on 06/Sep/20 $$\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{4}^{{n}} \:\left(\mathrm{1}−\mathrm{cos}\:\left(\frac{\alpha}{\mathrm{2}^{{n}} }\right)\right)\:?\: \\ $$$$\:\:\sqrt{{bemath}} \\ $$ Answered by bobhans last updated on 06/Sep/20 $$\:\:\:\underset{\mathrm{n}\rightarrow\infty}…
Question Number 177570 by mathlove last updated on 07/Oct/22 $$\underset{\Delta{x}\rightarrow{cos}\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\:\frac{{sin}^{\mathrm{3}} \left(\Delta{x}+{x}\right)−{sin}^{\mathrm{3}} {x}}{\mathrm{2}^{−\mathrm{1}} \Delta{x}}=? \\ $$ Commented by blackmamba last updated on 07/Oct/22 $$ \\…
Question Number 111960 by john santu last updated on 05/Sep/20 $$\left(\mathrm{1}\right)\underset{{x}\rightarrow\frac{\pi}{\mathrm{4}}} {\mathrm{lim}}\:\mathrm{sin}\:\left(\frac{\pi}{\mathrm{4}}−{x}\right).\mathrm{tan}\:\left({x}+\frac{\pi}{\mathrm{4}}\right)\:? \\ $$$$\left(\mathrm{2}\right)\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\:\frac{\pi\left(\pi−\mathrm{2}{x}\right)\mathrm{tan}\:\left({x}−\frac{\pi}{\mathrm{2}}\right)}{\mathrm{2}\left({x}−\pi\right)\mathrm{cos}\:^{\mathrm{2}} {x}}\:? \\ $$$$\left(\mathrm{3}\right)\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{3}{x}\left(\mathrm{cos}\:\mathrm{3}{x}−\mathrm{cos}\:\mathrm{7}{x}\right)}{\:\sqrt{\mathrm{sin}\:\mathrm{2}{x}+\mathrm{1}}\:−\sqrt{\mathrm{tan}\:\mathrm{2}{x}+\mathrm{1}}}\:? \\ $$$$\left(\mathrm{4}\right)\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\mathrm{2}{x}}{\mathrm{3}−\sqrt{\mathrm{3}{x}+\mathrm{9}}}\:? \\ $$$$ \\…