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Author: Tinku Tara

x-3-x-4-21-16-x-

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Question Number 216076 by efronzo1 last updated on 27/Jan/25 $$\:\:\:\frac{\lfloor\frac{\mathrm{x}}{\mathrm{3}}\:\rfloor}{\lfloor\:\frac{\mathrm{x}}{\mathrm{4}}\:\rfloor}\:=\:\frac{\mathrm{21}}{\mathrm{16}}\:;\:\mathrm{x}=? \\ $$ Answered by mr W last updated on 28/Jan/25 $$\lfloor\frac{{x}}{\mathrm{3}}\rfloor=\mathrm{21}{k} \\ $$$$\lfloor\frac{{x}}{\mathrm{4}}\rfloor=\mathrm{16}{k}\:\neq\mathrm{0}\:\Rightarrow{k}\neq\mathrm{0} \\ $$$$\frac{{x}}{\mathrm{3}}=\mathrm{21}{k}+{a}\:{with}\:\mathrm{0}\leqslant{a}<\mathrm{1}…

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Find-the-largest-value-of-the-non-negative-integer-p-for-which-lim-x-1-px-sin-x-1-p-x-sin-x-1-1-1-x-1-x-1-4-

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Question Number 216077 by MATHEMATICSAM last updated on 27/Jan/25 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{largest}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{non}\:\mathrm{negative} \\ $$$$\mathrm{integer}\:{p}\:\mathrm{for}\:\mathrm{which}\: \\ $$$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\left\{\frac{−\:{px}\:+\:\mathrm{sin}\left({x}\:−\:\mathrm{1}\right)\:+\:{p}}{{x}\:+\:\mathrm{sin}\left({x}\:−\:\mathrm{1}\right)\:−\:\mathrm{1}}\right\}^{\frac{\mathrm{1}\:−\:{x}}{\mathrm{1}\:−\:\sqrt{{x}}}} \:=\:\frac{\mathrm{1}}{\mathrm{4}}\:. \\ $$ Answered by mahdipoor last updated on 27/Jan/25…

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Question-216105

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Question Number 216105 by mr W last updated on 27/Jan/25 Answered by A5T last updated on 27/Jan/25 $$\mathrm{x}^{\mathrm{2}} =\mathrm{2}\left(\frac{\mathrm{x}+\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} \Rightarrow\mathrm{x}^{\mathrm{2}} =\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{1}}{\mathrm{2}}\Rightarrow\mathrm{x}^{\mathrm{2}} −\mathrm{2x}−\mathrm{1}=\mathrm{0} \\ $$$$\Rightarrow\mathrm{x}=\frac{\mathrm{2}\underset{−}…

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find-the-maximum-of-y-sin-x-sin-2x-

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Question Number 216074 by CrispyXYZ last updated on 27/Jan/25 $$\mathrm{find}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{of}\:{y}=\mid\mathrm{sin}\:{x}\mid+\mid\mathrm{sin}\:\mathrm{2}{x}\mid. \\ $$ Answered by efronzo1 last updated on 27/Jan/25 $$\:\mathrm{y}\:=\:\mid\mathrm{sin}\:\mathrm{x}\mid\:+\:\mathrm{2}\mid\mathrm{sin}\:\mathrm{x}\mid\:\sqrt{\mathrm{1}−\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}} \\ $$$$\:\:\mathrm{y}=\:\mid\mathrm{sin}\:\mathrm{x}\mid\:\left(\mathrm{1}+\mathrm{2}\sqrt{\mathrm{1}−\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}}\:\right) \\…

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