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Author: Tinku Tara

let-f-R-R-be-a-continuius-function-such-that-for-any-two-real-numbers-x-and-y-f-x-f-y-10-x-y-201-then-prove-that-f-2019-f-2022-2-f-2021-

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Question Number 148990 by gsk2684 last updated on 02/Aug/21 $${let}\:{f}:{R}\rightarrow{R}\:{be}\:{a}\:{continuius}\:{function} \\ $$$${such}\:{that}\:{for}\:{any}\:{two}\:{real}\:{numbers} \\ $$$${x}\:{and}\:{y}\:\mid{f}\left({x}\right)−{f}\left({y}\right)\mid\leqslant\mathrm{10}\mid{x}−{y}\mid^{\mathrm{201}} \\ $$$${then}\:{prove}\:{that} \\ $$$${f}\left(\mathrm{2019}\right)+{f}\left(\mathrm{2022}\right)=\mathrm{2}\:{f}\left(\mathrm{2021}\right) \\ $$ Terms of Service Privacy Policy…

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if-tg-0-5x-2-find-sin-x-2-cos-x-3-

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Question Number 148987 by mathdanisur last updated on 02/Aug/21 $${if}\:\:\:{tg}\left(\mathrm{0},\mathrm{5}{x}\right)\:=\:−\mathrm{2} \\ $$$${find}\:\:\:\frac{{sin}\left({x}\right)\:+\:\mathrm{2}}{{cos}\left({x}\right)\:-\:\mathrm{3}}\:=\:? \\ $$ Answered by EDWIN88 last updated on 02/Aug/21 $$\:\mathrm{tan}\:\left(\frac{\mathrm{1}}{\mathrm{2}}{x}\right)=−\mathrm{2}\:\rightarrow\begin{cases}{\frac{\mathrm{1}}{\mathrm{2}}{x}\:{in}\:\mathrm{2}^{{nd}} \:{quadrant}}\\{\frac{\mathrm{1}}{\mathrm{2}}{x}\:{in}\:\mathrm{4}^{{th}} \:{quadrant}}\end{cases} \\…

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The-nearest-distance-of-0-3-to-curve-y-6-x-2-is-

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Question Number 83445 by naka3546 last updated on 02/Mar/20 $${The}\:\:{nearest}\:\:{distance}\:\:{of}\:\:\left(\mathrm{0},\:\mathrm{3}\right)\:\:{to}\:\:{curve}\:\::\:\:{y}\:=\:\:\mathrm{6}\:−\:{x}^{\mathrm{2}} \:\:{is}\:\:… \\ $$ Commented by MJS last updated on 02/Mar/20 $${P}=\begin{pmatrix}{{x}}\\{{y}}\end{pmatrix}\:=\begin{pmatrix}{{x}}\\{\mathrm{6}−{x}^{\mathrm{2}} }\end{pmatrix};\:\mathrm{distance}^{\mathrm{2}} \:\mathrm{is}\:{x}^{\mathrm{2}} +\left(\mathrm{3}−{x}^{\mathrm{2}} \right)^{\mathrm{2}}…

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