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Category: Algebra

lim-x-pi-2-sinx-1-x-pi-2-

Question Number 169004 by mathlove last updated on 23/Apr/22 $$\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\left(\frac{{sinx}−\mathrm{1}}{{x}−\frac{\pi}{\mathrm{2}}}\right)=? \\ $$ Commented by infinityaction last updated on 23/Apr/22 $$\:\:\:\:\:\:\:\:\:\:\:\left({let}\right){p}\:\:\:\:\:\:\:\:=\:\:\:\:\:\:\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\:\left(\frac{\mathrm{sin}\:{x}−\mathrm{sin}\:\frac{\pi}{\mathrm{2}}}{{x}−\frac{\pi}{\mathrm{2}}}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{p}\:\:\:\:=\:\:\:\:\:\:\:\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\:\left\{\frac{\mathrm{2cos}\:\left(\frac{{x}+\pi/\mathrm{2}}{\mathrm{2}}\right)\mathrm{sin}\:\left(\frac{{x}−\pi/\mathrm{2}}{\mathrm{2}}\right)}{\mathrm{2}\left(\frac{{x}−\pi/\mathrm{2}}{\mathrm{2}}\right)}\right\}…

Question-37906

Question Number 37906 by mondodotto@gmail.com last updated on 19/Jun/18 Answered by tanmay.chaudhury50@gmail.com last updated on 19/Jun/18 $${join}\:{oB}\:{so}\:<{OBC}=\mathrm{90}^{{o}} \\ $$$$<{BEO}=<{OBE}={x}\left\{{since}\:{OB}={OE}={radius}\right\} \\ $$$${x}+\mathrm{18}^{{o}} +\mathrm{90}^{{o}} +{x}=\mathrm{180}^{{o}} \\ $$$$\mathrm{2}{x}=\mathrm{72}^{{o}}…

n-3-1-4-n-2-

Question Number 103436 by bramlex last updated on 15/Jul/20 $$\underset{\mathrm{n}\:=\:\mathrm{3}} {\overset{\infty} {\prod}}\left(\mathrm{1}−\frac{\mathrm{4}}{\mathrm{n}^{\mathrm{2}} }\right)\:=\:? \\ $$ Answered by Worm_Tail last updated on 15/Jul/20 $$\underset{\mathrm{3}} {\overset{{oo}} {\prod}}\left(\mathrm{1}−\frac{\mathrm{4}}{{n}^{\mathrm{2}}…

sin-pi-ix-sinh-pi-ix-0-Find-all-the-real-value-s-of-x-

Question Number 168881 by Eulerian last updated on 20/Apr/22 $$\:\mathrm{sin}\left(\pi\sqrt{\mathrm{ix}}\right)\:+\:\mathrm{sinh}\left(\pi\sqrt{\mathrm{ix}}\right)\:=\:\mathrm{0} \\ $$$$\: \\ $$$$\:\mathrm{Find}\:\mathrm{all}\:\mathrm{the}\:\mathrm{real}\:\mathrm{value}/\mathrm{s}\:\mathrm{of}\:\mathrm{x}. \\ $$ Answered by MJS_new last updated on 20/Apr/22 $$\mathrm{sin}\:{t}\:+\mathrm{sinh}\:{t}\:=\mathrm{0}\:\Rightarrow\:{t}=\mathrm{0} \\…