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Author: Tinku Tara

Question-212899

Question Number 212899 by vasil92 last updated on 26/Oct/24 Answered by MrGaster last updated on 02/Nov/24 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−{x}^{{n}} }{dx}=\mathrm{1} \\ $$$$=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left[{x}−\frac{{x}^{{n}−\mathrm{1}} }{\left({n}+\mathrm{1}\right)\centerdot^{\mathrm{2}}…

Question-212834

Question Number 212834 by efronzo1 last updated on 25/Oct/24 $$\:\:\:\:\underbrace{\:} \\ $$ Answered by golsendro last updated on 25/Oct/24 $$\:\:\mathrm{let}\:\begin{cases}{\mathrm{a}=\mathrm{sin}\:\mathrm{x}\:,\:\mathrm{b}=\mathrm{cos}\:\mathrm{x}}\\{\mathrm{c}=\mathrm{sin}\:\mathrm{y}\:,\:\mathrm{d}=\mathrm{cos}\:\mathrm{y}}\end{cases} \\ $$$$\:\:\mathrm{ac}\:+\:\mathrm{bd}\:=\:\mathrm{cos}\:\left(\mathrm{x}−\mathrm{y}\right) \\ $$$$\:\:\mid\mathrm{ac}+\mathrm{bd}\mid\:\leqslant\:\mathrm{1}\: \\…