Category: Algebra

Question Number 151660 by mathdanisur last updated on 22/Aug/21 Answered by Olaf_Thorendsen last updated on 22/Aug/21 $$\ln (e+\sin kx)=1+\ln (1+\frac{\sin kx}{e})\underset{0}{\sim }1+\frac{kx}{e}$$$$\frac{\mathrm{1}−\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}\mathrm{ln}\left({e}+\mathrm{sin}{kx}\right)}{{x}}\:\underset{\mathrm{0}} {\sim}\:\frac{\mathrm{1}−\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}\left(\mathrm{1}+\frac{{kx}}{{e}}\right)}{{x}}\:\:\left(\mathrm{1}\right)…

Question Number 151638 by mathdanisur last updated on 22/Aug/21 $$\underset{0}{\stackrel{2\mathit{\pi }}{\int }}{(1-\cos \mathbf{x})}^{10}\cos \left(10\mathrm{x}\right)\mathrm{dx}=?$$ Answered by Olaf_Thorendsen last updated on 22/Aug/21 $$\mathrm{I}\:=\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \left(\mathrm{1}−\mathrm{cos}{x}\right)^{\mathrm{10}}…

Question Number 20552 by ajfour last updated on 28/Aug/17 $$Therootsoftheequation$$$${(3-x)}^4+{(2-x)}^4={(5-2x)}^{4}are$$$$\left(a\right)allreal\left(b\right)allimaginary$$$$\left(c\right)tworealandtwoimaginary$$$$\left(d\right)noneoftheabove.$$ Answered by…

Question Number 20550 by Tinkutara last updated on 28/Aug/17 $$Findtheequationofcircleincomplex$$$$formwhichtouchesiz+\overline{z}+1+i=0$$$$andforwhichthelines(1-i)z=$$$$(1+i)\overline{z}and(1+i)z+(i-1)\overline{z}-4i=0$$$$arenormals.$$ Answered by…

Question Number 86085 by Serlea last updated on 27/Mar/20 $$\mathrm{If}{\mathrm{X}}^2+{\mathrm{Y}}^2=10$$$$\mathrm{XY}=5$$$$\mathrm{Find}({\mathrm{X}}^2-{\mathrm{Y}}^2)$$ Commented by jagoll last updated…