Category: Algebra

Question Number 207493 by hardmath last updated on 17/May/24 $$\underset{\mathbf{n}\to \mathrm{\infty }}{\lim }{\left(\frac{\mathrm{n}-1}{\mathrm{n}+2}\right)}^{\mathbf{n}+3}=?$$ Answered by A5T last updated on 17/May/24 $$\left(\frac{{n}+\mathrm{2}}{{n}−\mathrm{1}}\right)^{{n}+\mathrm{3}} =\left(\frac{{n}−\mathrm{1}+\mathrm{3}}{{n}−\mathrm{1}}\right)^{{n}+\mathrm{3}} =\left(\mathrm{1}+\frac{\mathrm{3}}{{n}−\mathrm{1}}\right)^{{n}+\mathrm{3}} \…

Question Number 207462 by hardmath last updated on 16/May/24 $$4\sin \frac{\mathbf{x}}{2}=1\mathrm{find}:\mathbf{x}=?$$ Commented by Frix last updated on 16/May/24 $$x=4n\pi +{2\sin }^{-1}\frac{1}{4}\vee x=2(2n+1)\pi -{2\sin }^{-1}\frac{1}{4}$$ Terms…

Question Number 207450 by York12 last updated on 15/May/24 $$\mathrm{Find}\mathrm{the}\mathrm{relation}\mathrm{between}m\mathrm{and}n\mathrm{for}\mathrm{which}\mathrm{the}\mathrm{following}\mathrm{holds}$$$$\frac{d\left(y\right)}{d\left(x\right)}{\mid }_{x=n}={\left(\frac{d\left(x\right)}{d\left(y\right)}{\mid }_{y=m}\right)}^{-1}$$ Answered by mr W last updated on 15/May/24 Commented…

Question Number 207385 by hardmath last updated on 13/May/24 $$\mathrm{Find}:$$$$\sqrt{{(2,5-\sqrt{5})}^2}-\sqrt[3]{{{(1,5-\sqrt{5})}^3)}^{\frac{1}{2}}}-\sqrt{2}\sin \frac{7\pi }{4}$$ Commented by Frix last updated on 13/May/24 $$=\frac{\mathrm{7}}{\mathrm{2}}−\sqrt{\mathrm{5}}−\frac{\sqrt{\mathrm{6}\left(−\mathrm{3}+\mathrm{2}\sqrt{\mathrm{5}}\right)}}{\mathrm{4}}−\frac{\sqrt{\mathrm{2}\left(−\mathrm{3}+\mathrm{2}\sqrt{\mathrm{5}}\right.}}{\mathrm{4}}\mathrm{i}…

Question Number 207407 by hardmath last updated on 13/May/24 Commented by Frix last updated on 13/May/24 $$2.\dots =2\sqrt{3}\cos 10°$$ Commented by Frix last updated on…