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Author: Tinku Tara

Question-131620

Question Number 131620 by mohammad17 last updated on 06/Feb/21 Answered by Dwaipayan Shikari last updated on 06/Feb/21 $$\underset{{z}\rightarrow\mathrm{2}{e}^{\frac{{i}\pi}{\mathrm{3}}} } {\mathrm{lim}}\frac{{z}^{\mathrm{3}} +\mathrm{8}}{{z}^{\mathrm{4}} +\mathrm{4}{z}^{\mathrm{2}} +\mathrm{16}}=\underset{{z}\rightarrow\mathrm{2}{e}^{\frac{{i}\pi}{\mathrm{3}}} } {\mathrm{lim}}\frac{{z}+\mathrm{2}}{{z}^{\mathrm{2}}…

for-pi-lt-x-lt-pi-2-find-the-solution-of-sin-x-gt-sin-x-2-2-sin-x-1-

Question Number 131622 by rydasss last updated on 06/Feb/21 $${for}\:-\pi\:<\:{x}\:<\:-\:\frac{\pi}{\mathrm{2}}\:{find}\:{the}\:{solution}\:{of} \\ $$$${sin}\:{x}\:>\:\:\frac{{sin}\:{x}\:+\:\mathrm{2}}{\mathrm{2}\:{sin}\:{x}\:+\:\mathrm{1}} \\ $$ Answered by mr W last updated on 07/Feb/21 $$−\pi<{x}<−\frac{\pi}{\mathrm{2}}\:\Rightarrow\:−\mathrm{1}<\mathrm{sin}\:{x}<\mathrm{0} \\ $$$${case}\:\mathrm{1}:\:\mathrm{2sin}\:{x}+\mathrm{1}>\mathrm{0},\:{i}.{e}.\:\mathrm{sin}\:{x}>−\frac{\mathrm{1}}{\mathrm{2}}…

Question-66082

Question Number 66082 by aliesam last updated on 08/Aug/19 Commented by mathmax by abdo last updated on 09/Aug/19 $${let}\:{I}\:=\int_{−\infty} ^{+\infty} \:{xsin}\left({x}^{\mathrm{3}} \right){dx}\:\Rightarrow{I}\:=\mathrm{2}\int_{\mathrm{0}} ^{\infty} \:{x}\:{sin}\left({x}^{\mathrm{3}} \right){dx}…